Mr Carson, 28, was shot in the head by a gang of men who burst into his family home in Walmer Street, in the south of the city, last Thursday night.
Francis Gerard Smith, from Springfield Road, Belfast, has been charged with possessing a rifle and 50 rounds of ammunition in suspicious circumstances.
Mr Smith was remanded in custody.
Two other west Belfast men have already been charged with murdering Mr Carson.
The murder accused - 37-year-old Michael Smyth, from Ardmonagh Gardens, and 32-year-old David Smyth, from Monagh Drive - were remanded in custody at Belfast Magistrate's Court on Tuesday.
Appearing before the same court on Wednesday, 39-year-old Francis Gerard Smith acknowledged supporters in the courtroom with a thumbs-up signal.
An investigating detective told the judge she could connect him to the weapons charges.
A defence solicitor put no questions to the officer and made no application for bail.
The judge remanded Francis Smith in custody until 30 March.
A man has appeared in court accused of having a rifle and ammunition in a case linked to the shotgun murder of Stephen Carson in Belfast last week.