I understand that this is a real concern for those on blood thinners and through my years of practice, I have treated a lot of patients on blood thinners and they did fine with their acupuncture treatments.
So can you get acupuncture if you are on a blood thinner? Yes, unless your doctor has advised otherwise. Acupuncture needles are so thin that if they happen hit a small capillary or get a drop or two of blood, the hole closes quickly behind the removal of the needle. As I am removing needles, I always have a cotton ball in one hand so if I see a little drop of blood, I quickly apply firm pressure and it will stop within a few seconds. Easy peasy!
Feel free to check out this short little article here too.