No he didn't, he wrote that in his yearbook, but the club never existed.
The Daily Mail's report is based on Gorsuch's yearbook which says he was the founder and president of the Fascism Forever Club
President of the Yard, Student Government: English Class Representative 1, Border Council Member 2; Executive Council Member 3; Forensics 1, 2, 3 (National Champi-on), 4 (Vice President); International Relations Club 2 (CO-founder), 3 (Vice President), 4 (President of O.A.S.); Dramatics 2 (The Odd Couple); How to win by a landslide 3, 4; YES 4; "Lousy Spanish Student" 2, 3, 4; Fascism Forever Club (Founder and President) 1, 2, 3, 4; Believer in The World According to Ward; Committee to reform The Beast (President) 2, 3, 4; "The carrousel ride is over" (or is it?) 4; I am not an alkie; I never wrote a debate case!
(source: snopes.com)
However, as Snopes have checked and reported such a club never existed in Georgetown Prep:
We contacted Georgetown Preparatory School to verify whether a "Fascism Forever" club operated in or around that school in 1985, and director of communications Patrick Coyle told us that “no such club ever existed" there.
It could be the case that the yearbook entry was merely a joke that referenced a non-existent "Fascism Forever" club, or that such a club existed but was an informal and unofficial one not sanctioned by the school, but we've found no evidence documenting either of those possibilities yet either.
America, The Jesuit Review1 gives more details and testimony that this was a joke aimed at Gorsuch's disagreement with the liberal views of the school staff.
Mr. Gorsuch [...] participated in the informal debates, where he was routinely teased, accused of being “a conservative fascist.” No shrinking violet, he would shoot back, taking on the liberal ethos of the school and even arguing with religion teachers about the liberal theological trends in vogue at the time.
[...]
When it came time to write his senior biography for the yearbook, he would make light of the divide between his conservative political beliefs and those of the more liberal faculty and students.
He wrote that he founded and led the “Fascism Forever Club,” though those with knowledge of the school back in the 1980s say there was no such club. The mention of it in the yearbook was a tongue-in-cheek attempt to poke fun at liberal peers who teased him about his fierce conservatism.
It was “a total joke,” said Steve Ochs, a history teacher at Georgetown Prep who was the student government advisor during Mr. Gorsuch’s junior and senior years at the Bethesda, Md., school.
“There was no club at a Jesuit school about young fascists,” he told America [The Jesuit Review]. “The students would create fictitious clubs; they would have fictitious activities. They were all inside jokes on their senior pages.”
1 - Georgetown Preparatory School is a Jesuit school.
