Rodriguez joins his fellow countryman Oscar Garcia, with the Brighton boss saying that the player will bring much-needed competition to his strike force.
"He's shown throughout his career he is capable of scoring goals," Garcia told the club's official website. "He can play in all attacking positions.
"The challenge for him now is to push for a place in the team and prove between now and the end of the season he is worth a longer-term deal with the club."
Brighton are currently eighth in the Championship.