Feltscher, who has 16 caps for Venzuela, played for Switerland at U19 and U21 level.
Neil Warnock said the free agent had trained with the Bluebirds "for a few weeks" before a deal was done.
The Switzerland-born 27-year-old left Spanish club Getafe in August, 2017, having also played for Real Zaragoza.
Warnock said: "We wanted to see him in a couple of games but he's done well and offers us some good cover and competition at the back."
