No, The Cramps is not a goth band, because they play Psychobilly, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy The Cramps are Bauhaus, Red Lorry Yellow Lorry, and The Danse Society.