No.
in order for a human to be inducted as a scout and later a marine he has to undergo mental conditioning as well as physical.
A Blank couldn't be screened by the psykers and therefore not be eligible for becoming a Space Marine.
We see a glimpse of becoming a Space Marine in Space Wolf novels.
(Yes they are not conventional), but the process itself couldn't be that much different from other chapters.
The complete "standard" process is here .
The Space Wolves have another ritual called "passing the gates of Morkai ".
In this test the Librarians take over the mind of an aspirant and judge it worthy or NOT worthy.
If any other chapters have similar tests Blanks would not be permitted to become Space Marines.
They certainly can't become Space Wolves.
Also we see the effect that Blanks have on psykers in the Eisenhorn and Ravenor trilogies.
So any aspirant trying out for the Space Marines would be found out fairly quick and either killed outright or passed on to the Black ships.
scifi.stackexchange.com/users/15632/Cherubel
Yes
But we have only ONE occasion of Blank in whole Wh40k literature.
It is introduced in the novel Emperor's Gift from Aaron Dembski-Bowden at chapter eleven, when Grey Knights Chapter marines arrive to Titan - their Chapter monastery planet, to give away the body of their fallen brother to be buried in Dead Fields.
There battle-brothers met Phlegyras - a so-called Ferrymen who’s work concludes in giving a proper ritual and burial to the fallen.
These men do not serve in any kind of battle roles.
Grey Knights immediately recognized Space Marine-like body type of this ferryman, and his unnatural aura of nothingness because he was a blank.
But anyways, no matter questions asked, Phlegyras never revealed who he was and how he became a Blank.
At any occasion, it is impossible to say how it is possible.
Gene-seed implantation to a naturally-born blank will result in immediate death because of psi-infused nature of gene-seed (please remember who their Grandfather is).
At least, that's the most popular theory the imperial scholars have.
So Phlegyras should become pariah after initiation to the Chapter.
scifi.stackexchange.com/users/110877/Владимир Истомин
In the Space Marine video game Captain Titus is a Blank.
He holds a warp generating device and fights an almost-daemon price with no mutation.
His immunity to the warp gets the Inquisition alerted by Leandros.
scifi.stackexchange.com/users/45957/Pyrowolf117
Nope, it's never happened.
And it never would because they're too valuable / rare / un-likeable to become Space Marines
As a male in the 40k universe, you have a 1 in 2 billion chance of being born with the Pariah Gene , so when one pops up, the Inquisition will always be the first on the scene.
And even if the Pariah were born on a chapter's recruiting world, chances are he would be rejected out right.
Obviously the chapter's Liberians would detect the Pariah immediately and either hand him over to the Inquisition or possibly kill him, depending on the chapter.
But some chapters don't employ any psykers at all, The Black Templars for example.
I'm sure they'd have other tests to check for Chaos or corruption but if a Pariah did pass these tests, they'd have another problem.
Pariahs give off an aura which makes people instantly and intensely dislike and distrust them.
They couldn't possibly be part of a squad when every one of their brothers permanently despises them.
scifi.stackexchange.com/users/20393/Daft
Alexandros the Blind, the current chapter master of the Sons of Dorn is a Blank.
scifi.stackexchange.com/users/94157/Carolus Rex
Another possible explanation is that they simply wouldn't be chosen.
A typical Chapter controls several recruiting worlds which may have populations in the millions or billions.
From this, they derive a very small number of recruits every year: given what we know of Chapter sizes and Space Marine lifespans and loss rates (when not appearing in other factions' codices, at least), it might be in the single digits.
So they can afford to be extremely choosy, with literally millions of people passed over for every one accepted.
At the same time, because normal human empathy is to some degree psychic, Blanks are not accepted by others around them - including, we must assume, Space Marines.
Even if the Blank is superlatively capable, the examining Marine will invent a flaw, simply because of his innate dislike of the Blank.
Since by definition everyone who makes the shortlist to be inducted is exceptional, it wouldn't take much to tilt the examiner's decision away from the Blank.
scifi.stackexchange.com/users/100151/Cadence
No, because such a person would be immediately picked up on by the Chapter's Librarians.
There are no examples of what happens next if such an individual is found: perhaps they are killed, or handed over to the Inquisition.
scifi.stackexchange.com/users/28642/Thomas Jacobs
Are there any instances in literature of Blanks/pariahs serving as Space Marines? Surely they'd be unstoppable when facing warp entities. I know assassins can be blanks and they're rare, etc.
Are there any instances of Blanks serving as Space Marines?
scifi.stackexchange.com
<warhammer-40k>
scifi.stackexchange.com/questions/79876
scifi.stackexchange.com/users/36763/Neil Hanvey
This is contested. Some claim that Blanks cannot become Space Marines because they cannot be screened by psykers. However, Captain Titus is a Blank in the Space Marine video game and the Space Wolf novels give a glimpse of one becoming a Space Marine. Although a Blank technically can’t become a space marine since the psykers and the Chapter’s Librarians would prevent this, the Space Wolf novels introduce the concept of Blanks becoming Space Marines, and Captain Titus and Alexandros the Blind may fall into that category. 
A Blank can’t become a space marine since the psykers and the Chapter’s Librarians would prevent this. The Space Wolf novels introduce the concept of Blanks becoming Space Marines. Captain Titus features as a Blank in the Space Marine video game and Alexandros the Blind is a Blank though there is no confirmation he is a Space Marine. 