The move is with a view to a longer-term contract with The Glovers for the former Farense and Southampton hit-man, who was recently playing with Greek club Ionikos.
Rodrigues had loan spells with Bournemouth and Bristol City, but his time with The Robins was cut short by a leg facture suffered with the Second Division side.
He will team up with fellow compatriot Hugo Rodrigues at the Somerset-based outfit.
"I want to give Danny the opportunity to get his fitness back to the level he had at Southampton," Yeovil boss Gary Johnson told the club's official website.
"If I can get him back to anywhere near that level of fitness, we will have signed a very good player."
Another player to join The Glovers on deadline day is young Wolves defender Nathan Talbott, who moves to Yeovil until the end of the season after being released by the Molineux club.
The pair's arrival is coupled with the departure of Lee Elam on loan to Conference leaders Chester City for the rest of the season.
The winger only joined The Glovers last November from Halifax Town but a lack of first team action has prompted him to join the Deva Stadium side.
Meanwhile, Johnson is running the rule over two trialists in training this week.
Southampton defender Jamie Gleeson and Leicester City defender Nick Matthews are all receiving run outs with the club.
