Welcome to the CAC!
Yes, you will have to buy a scan tool to read your codes. Make sure to look for a CAN (controller area network) enabled scan tool. Most new ones are; however, some older ones are not.
Keep in mind that most scan tools will only read powertrain control module (P) codes. If you have an ABS light (C codes), you would need a scan tool with added abilities. Actron sells one that reads only C codes(CP9449) and Innova sells a tool that scans P and C codes (Innova 3150).
Hope all of this info helps and I am sure others will add more.
You picked a good place to find information about your corvette.