There are plenty of daft rules and regulations in the world of commercial aviation, but a tattoo ban is not one of them.
However, any sort of overt tattoo won't do much for you career prospects, and the reason is very, very simple. Hang around an airport for a while and see what all the pilots look like. With very few exceptions we will be smartly and conservatively dressed, because that's the image that airlines want us to project - and it's what joe public expect to see. Knuckles with 'love' and 'hate' etched into them or a spiders web on your shaved skull are unlikely to get you extra marks at a job interview.