The 33-year-old has been a free agent since leaving Birmingham City in November.
Clayton started his career with Manchester City but did not make a senior appearance.
He switched to Leeds United, initially on loan in 2010 before making his move permanent. Loans with Peterborough United and MK Dons followed before he became a regular at Elland Road.
After failing to agree terms on a new contract, he joined Huddersfield Town for a reported £350,000 in 2012.
Clayton made 94 appearances for the Terriers across two years before joining Middlesbrough in a £1.5m deal in 2014, beginning a six-year stay on Teesside. He made 241 appearances for Boro, playing a major role in their promotion to the Premier League in 2016.
Clayton made 34 appearances in the top flight, with all but two being starts.
He joined Birmingham City - and his former Boro boss Aitor Karanka - in the summer of 2020 but made only 16 appearances before his contract was terminated in November.
His last senior game came in January 2021.