The 32-year-old Scotland international had trained with Kilmarnock after leaving Nottingham Forest.
Staggies boss Jim McIntyre told the club website: "We are delighted to announce the signing of Chris.
"He will provide much-needed competition on the flanks for us. He also brings a wealth of experience playing at the top level."
Burke came to prominence with Rangers, scoring on his debut in a 5-0 win over Kilmarnock in 2002.
A lack of first-team football at Ibrox brought about a move to Cardiff on a free transfer in January 2009. He made more than 100 league appearances for the Bluebirds before switching to Birmingham for three seasons where he scored 28 goals in 155 appearances.
Burke then played 50 league games for Nottingham Forest across the past two seasons, during which time he had a loan spell at Rotherham before becoming a free agent in the summer.
Ross County have signed the former Rangers, Cardiff and Birmingham winger Chris Burke until the season's end.