The 31-year-old, had been without a club after his contract was terminated by the French club Nantes in August.
He hopes the move will help him play a role for Burkina Faso in qualifying for the Africa Cup of Nations.
“I have come to a group of fighters, hopefully the determination will benefit club and country,” he said.
“The current position is not the desired spot for the club, I want to fight to ensure the club remain in the big league.”
Burkina Faso must win their final Nations Cup qualifier against visiting Mauritania, who have already reached the finals, if they are to have any chance of qualifying to play in Egypt.
Newly-promoted Rizespor, based in the eastern part of the Black Sea Region of Turkey, are currently bottom of the 18-team Super Lig.
Nakoulma also has previous experience in Turkish football after spending two years with Mersin Idmanyurdu between 2014 and 2016 and that was followed by a short stint in the top flight with Kayserispor in 2016.
He was a key part of the Burkina Faso side which finished the 2013 Africa Cup of Nations as surprise runners-up.
Nakoulma also played a key role and scored twice as the Stallions finished third at the 2017 edition of the Nations Cup tournament in Gabon.
He has 52 caps for his country, scoring 13 times – including a hat-trick in a 4-0 home win over Cape Verde in a 2018 World Cup qualifier in November 2017.