Ahoy, Costco member! No, Costco does not currently install or replace car batteries.
You can, however, buy a car battery at Costco—and Costco’s prices are typically very competitive!
Once you buy a battery from Costco, you can bring it to another auto service shop to get it installed. It’s pretty straightforward to install the battery yourself, too, if you have an hour and the right tools (socket wrench, adjustable wrench, pliers).
Good luck with your battery replacement!