Jingles on rock stations in the US have been rare.
The Doubleday stations in the early 1980s (then WAPP NYC, WMET Chicago, WLLZ Detroit, WAVA Washington, KWK St Louis, KDWB-FM Minneapolis, KPKE Denver) did experiment with a TM jingle package that sounded like the music they were playing. Most of those stations got crushed when Top 40 had a big ratings resurgence in 1983/84 (not that the jingle package had anything to do with that).
There has been some ironic use of jingles over the decades. In the late 90s/early 2K, a few mainstream/active rock stations produced old-timey PAMS jingles with snarky attitude-driven lyrics. That fit the boys-club imaging of the time in that format. Recall one with lyrics "the station to listen to while you're having unsafe sex." These didn't have a lot of shelf life though, and didn't last long on the air.
Alternative stations have done in-house sung IDs over songs from the format. These were not really traditional jingles, but some very creative stuff at times. More ironic/tongue in cheek, appropriate to the format.