Can you faint from getting a tattoo?

yes

For women it may be due to their menstrual cycle

for all it may be due to lack of food or drink or nerves or low blood pressure or being a little under the weather.

As soon as the endorphins kick in and for the first ten to twenty minutes it may make you feel a little rush or a little woozy. I find it best to try and completely relax and listen to music I love. I learnt to meditate to help with the tattooing process and it helps me.