The Australian right-back, 25, has signed until January after joining on trial.
He played the full 90 minutes of the Lincolnshire Senior Cup final win over Grimsby Town but was clearly lacking match fitness. He was part of the reserves squad that headed to Middlesbrough on Tuesday for their opening game of their season.
Cliff Byrne and Eddie Nolan look to be ahead of him in the pecking order for a first-team place, but McClenahan is confident of pushing them for a place in matchday squads.
"It's good to have competition here. It's a tough league, there are a lot of games and I think it's important to have a number of players here who can perform in numerous positions," he told United's official website.
"When players get suspended or injured you need to have back-up so hopefully I can take my chance when the opportunity comes."
Source: PA