The Spanish defender was signed on a short-term deal earlier in the season by previous manager Gary Jardine following his release from Ladbrokes Premiership side Hamilton in the summer.
Garcia Tena, who has previously been on the books at Espanyol and Italian giants Juventus, has made ten appearances for City.
The club also announced that Liam Henderson will be departing in order to continue his career in Australia. The former Hearts youngster joined on loan from Falkirk in November, and had recently signed as a permanent City player until the end of the season. He heads Down Under to join Perth-based outfit Stirling Lions, who play in the National Premier Leagues Western Australia. The move affords Henderson the chance to combine playing with coaching and City have reluctantly allowed him to terminate the remainder of his contract.