Tyga -- Cyber-Offensive to Find Kidney for Sick Kid

Tyga is on a mission to find a kidney, ASAP ... and it's all because he's determined to help a sick kid he met during a recent visit to an L.A. Children's Hospital ... TMZ has learned.

We know ... Tyga recently surprised 60 kids with all sorts of gifts and goodies, including fresh clothing, music and Flips headphones.

But during the visit, the rapper spent some time with a brave kid named Isael ... who's hoping to find a kidney donor so he can have a life-saving transplant.

We're told Tyga was so moved by Isael's story, he swore he would do everything he could to help the kid find a match ... starting with reaching out to his fans on Twitter and Instagram.

Meanwhile, over in Detroit ... another rapper, Big Sean, was spreading Christmas cheer at the Children's Hospital of Michigan.

We're told Big Sean hit up a local Toys R Us and went on a shopping spree for the kids ... buying up board games, stuffed animals, dolls, headphones and more.

A source at the hospital tells TMZ ... Big Sean also made a 5-figure donation to the children's ward.