Reid, who has previously played for Stourbridge and Rushall Olympic in the Southern League Premier Central , left fellow National League North side Leamington earlier this month.
The forward made 13 appearances for Leamington in the league, nine of which were starts, during his short spell with the club, but did not get on the score sheet.
He did score the winner in their FA Trophy game against Bishop’s Stortford back in November.
Paul Holleran, the manager of Leamington, praised the forward’s ‘application’ and ‘work ethic’ in a statement when Reid left the club at the start of the month
He said: “I would personally like to thank Rackeem for all his efforts during his time with us. He is a super young man whose application, work ethic and attitude has been first class, and we wish him all the best in the next stage of his career.”
He now joins the Bucks on a short-term deal, giving boss Kevin Wilkin more options in forward areas as they battle to beat relegation – they currently trail 20th-placed Buxton by nine points having played the same number of games.