The 30-year-old joins the club until the end of the season and will provide Rennie with a steady option at centre back or left back.
He could make his debut on Sunday afternoon against Alloa Athletic.
A club spokesperson said: “Falkirk Football Club is delighted to announce the signing of Aaron Taylor-Sinclair.
“The 30-year-old defender joins The Bairns on a deal until the end of the season and goes into contention for Sunday’s cinch League One match against Alloa Athletic.
“Aaron has been capped at international level for Antigua and Barbuda, featuring in their 1-0 win over Grenada this year in the World Cup 2022 Qualifiers.
"A left sided defender who can play at both left centre back and left back, Aaron began his career with Montrose before joining Partick Thistle, where he played an key role in their 2012/13 First Division win.”