How long after I get my tongue pierced can I have an alcoholic drink?

Don't do it . Tongue studs can damage your teeth and may be swallowed . I have seen patients who had this happen to them. The alcohol issue just depends on how long the area takes to heal as it may be sensitive while it's raw.
Give it a week. Wait about a week for the area to heal otherwise the alcohol will not only hurt when you drink it but impair healing. I am not a big fan of tongue piercings as I have seen multiple complications including life threatening infections and bleeding. I have also seen patients develop recurring throat infections and tonsillitis who never had it before getting their tongues pierced.
Soon. After i perform tonsillectomies i generally tell my patients they caeat or drink whatever they want to.... You body (and your piercing, for that matter) will tell you if it is the right thing. There might be a little pain with some alcohol after the piercing, but i don't think it woud be that big of a deal to have a drink right after...