Based on a lazy google search it seems he's never commented on the issue. But, come on, first ever AnCap president, there's no way he doesn't at least try and do something.
Also learned from google, apparently he's somewhat pro-gay right, but in the typical libertarian "mind your own business" way, which I guess is better than blatant bigotry 
He's a massive queerphobe who openly fights against anti-discrimination laws and wants to abolish quotas for trans people in public service, except that ofc he doesn't say "trans people" but uses a slur. This isn't surprising, either, all forms of libertarianism are inherently at odds with the rights of marginalized people. They'll always place free speech bs and the freedom of businesses to discriminate first, and their understanding of civil rights in general will always inherently favor those already in power.
Yeah, like I said it was a lazy google search, I saw some quotes saying he was alright with gay marriage but under a "none of my business" logic. Like most AnCap types that usually bullshit, he's fine with the rich being bigots if they want to.