The German high-speed train model capable of tilting is the ICE T.
ICE T trainsets use active tilting technology to lean into curves. This allows them to negotiate winding conventional railway routes at higher speeds and with greater passenger comfort than a comparable non-tilting train could normally provide.
The trains consist principally of Deutsche Bahn classes 411 and 415. They were developed in the 1990s for long-distance services on existing lines, complementing the faster ICE trains designed primarily for dedicated high-speed routes. ICE T entered passenger service in 1999 and has a maximum speed of about 230 km/h.
The ICE 3 and ICE 4 are different models and are not the standard answer to this question. Another small source of confusion is the letter T: it is commonly associated with “tilt,” but the project was originally known as IC T, referring to a self-propelled InterCity train. The branding changed to ICE T shortly before service began.