The American goalkeeper moved to the West Yorkshire outfit on a two-year contract last month.
The 20-year-old made his debut for Leeds on Friday evening, when he came on as a substitute in the second half of the pre-season friendly against Harrogate Town away from home.
Horton replaced Marco Silvestri in the 74th minute at the CNG Stadium and gave a good account of himself during the 1-1 draw.
The goalkeeper was happy to make his debut for the Whites and posted the following message on Twitter:
Horton is a talented young goalkeeper, but it will not be easy for him to break into the first team and play regularly for Leeds during the 2015-16 campaign.
That’s mainly because in Marco Silvestri the Championship outfit have a goalkeeper who is probably good enough to play in the Premier League.
The 24-year-old Italian custodian was one of the best players for Leeds last season.
The former Chievo player featured in 43 appearances in the Championship, keeping 12 clean sheets in the process.
Silvestri made 3.07 saves per game and 2.36 saves per goal on average, and it will be tough for Horton to get the nod ahead of him in the 2015-16 campaign.