The 22-year-old left back who has made one first team appearance has moved to Valley Parade until the end of the season.
Tierney has previously been on loan at Crewe and Colchester and Bradford manager Colin Todd said he was delighted to have the player:
"Paul is another valuable acquisition to the football club who we will have available for the rest of the season," Todd told the club's official website. "He comes with a fine pedigree and has a good left foot. Signing him puts more competition on places and we look forward to him being part of a squad to keep pushing for a play-off place in the league."