I have a canning book by Ball my grandma bought me for my birthday. There is a recipe in it for BBQ Sauce and it says: Process half-pints and pints 20 minutes in a boiling-water canner. So I would say yes, you can.
You sure can! My canning group has LOTS of BBQ recipes that they can. I may use some of my tomato sauce to do some after I get done making and canning ketchup.
Ok good... I have a tomato based sauce I like on my chicken, and I shared some with a friend, and she love sit too.... So I want to make sure if I make a whole lot to share with her again, I just can the rest for myself for the next year and not have to sit and heat it up fresh everytime I want it!
Please make sure your recipe is an approved recipe to can, you cannot just can any old recipe, there are a lot of issues to deal with, if you make a sauce you like, freeze it unless you use a recipe from a reliable source, like the ball blue book.
You can waterbath can BBQ sauce ONLY IF IT IS ACID ENOUGH.
Not all recipes are.
Best thing is to use a tested, modern recipe that a responsible source (Ball, extension service, etc) bills as safe for waterbath canning.
If you really like your own recipe, you should test its pH before deciding whether it can be done that way -- but especially with something thick and colored like bbq sauce this really ought to be done wiht a proper (and properly calibrated) pH meter, not the little litmus strips that turn colors.