You'll have to complete the Eden Prime mission to recruit Wrex in "Mass Effect." Shepard talks with Captain Anderson after waking up on the Normandy about Saren and his possible motives for allying with the Geth and attacking Eden Prime. Anderson will tell you to tell Joker to take the Normandy to the Citadel, where you will be able to speak with the council about Saren and his plans. Wrex will be in the C-Sec offices, but you can't travel straight there and speak with him. You must complete a few steps before he'll be available to recruit.
Travel to the Citadel. You will see a cut scene of Udina talking to the council in his office about Eden Prime. Udina and Anderson will tell you to meet them at the Citadel Tower to testify in Saren's trial.
Go to the top floor of the Citadel Tower. Anderson will meet you at the stairs to the council platform. Captain Anderson will suggest after the hearing that you speak with Barla Von, a Volus who works for the Shadow Broker.
Speak to Barla Von in the Financial District. Barla Von will tell you the Shadow Broker hired a Krogan Battlemaster to eliminate Saren after Saren betrayed him. He'll tell you the Krogan has been picked up by C-Sec and may still be in their offices.
Go to the C-Sec offices. The elevator down to the C-Sec offices is located beneath the Citadel Embassies.
Approach Wrex in the C-Sec office. This will trigger the dialogue that allows you to recruit Wrex. Wrex will offer his services if you help him take out Fist in Chora's Den. Agree to his offer and Wrex will join your party.