The 22-year-old joins the Yorkshire side on a two-year contract, as part of their revamp under new head coach Ryan Carr.
Weaver played 11 NRL games over three seasons for the Titans before being released by them last month.
His arrival follows the surprise departure of hooker Liam Horne to Leigh Leopards, while Mikaele Ravalawa, Semi Valemei and Blake Taaffe have already joined the Tigers for next season.
Cas director of rugby Chris Chester told the club website, external: “He’s the final piece of our spine for 2026.
“Tom is an organising, on-the-ball number seven who has a strong running and kicking game.
“I know Ryan can take Tom’s game to a whole new level, and I’m really looking forward to seeing him get to work in pre-season.”
