The goalkeeper, who played for France at junior level, made the switch after the move was approved by world governing body FIFA last month.
Luca, who plays for Spanish second-division outfit Granada, qualified for the North African country through his father, whose parents originated from the Kabylie region of Algeria.
The 27-year-old was called up for the matches against Somalia on October 9 and Uganda five days later.
Algeria lead Group G with 19 points, four ahead of nearest rivals Uganda. A win in either of the two remaining matches would secure qualification for next year's finals in North America.