Section 18C of Australia's Racial Discrimination Act makes it illegal to insult someone because of their race.
Senator David Leyonhjelm, a libertarian, says Section 18C damages free speech and should be repealed.
But he has lodged a complaint under the law in an attempt to prove a point.
Newspaper columnist Mark Kenny made the "angry white male" comments in an article that also labelled Mr Leyonhjelm a "boorish, supercilious know-all with the empathy of a besser block".
Mr Leyonhjelm said that while he was not offended by the comments, he saw an opportunity to demonstrate why Section 18C should, in his opinion, be repealed.
"Under the Act, Mr Kenny's article is unlawful because his article was reasonably likely, in all the circumstances, to offend, insult, humiliate or intimidate another person or a group of people on the basis of their colour," he said in a statement.
He said the comments were "reasonably likely â€¦ to offend or insult some white males".
"Assuming the adjudicators at the Human Rights Commission are guided by the law and not racists, I anticipate the complaint should succeed. Of course, if I succeed in having Section 18C repealed, Mr Kenny will be free to insult me as much as he likes," the statement said.
Section 18C says that a person cannot publicly "offend, insult, humiliate or intimidate" another person or group because of their "race, colour or national or ethnic origin".
Conservatives have campaigned against the law since it was used to prosecute prominent right-wing commentator Andrew Bolt.
Former Prime Minister Tony Abbott said he would repeal Section 18C in 2013, but later abandoned his attempt amid strong opposition.
Mr Abbott reignited debate this week when he said he should have pursued a less ambitious reform that removed the words "offend" and "insult" from the law.
An Australian politician has lodged a complaint with the country's Human Rights Commission after a newspaper article labelled him an "angry white male".