The 34-year-old, who played for the Clarets from 2015-16, left Scottish Premiership side Rangers in November.
In the same month, he was given a one-match ban for breaking Scottish FA rules on gambling and has since been charged with misconduct by the FA.
Barton is available for Saturday's FA Cup tie against Sunderland, registering in time to serve his ban on Monday.
The midfielder joined Rangers on a free transfer in the summer but only made seven appearances for the Ibrox club.
The former Manchester City, Newcastle and Queens Park Rangers player had his contract terminated following a training-ground altercation in September.
Last month, the FA claimed he broke rules by placing 1,260 bets on "football matches or competitions" between 26 March 2006 and 13 May 2016.
Burnley have re-signed Joey Barton for the remainder of the season despite the threat of a Football Association ban.