Ganesha is a popular figure in Hindu art dating back centuries. Ganesha is depicted in poses from sitting to dancing, at rest with his family and even battling demons.
Hindu religion as a whole does not disallow tattoos. Sects will differ, and keep in mind that Hindu cultural values are rather conservative on most things. Even though tattoos are now commonly accepted, there is still a bit of rebelliousness and an independent streak running through most people who get them.