Yes, there are tests for COVID-19. The FDA has created this easy-to-understand information about the different types of coronavirus tests and the FDA’s role in authorizing them (download this PDF).
Though there is currently no FDA-approved or cleared test for COVID-19, the FDA has issued several Emergency Use Authorizations (EUAs). During public health emergencies declared under section 564 of the FD&C Act, the FDA is able to issue EUAs when certain criteria are met that allow for the use and distribution of potentially life-saving medical products to diagnose, treat, or prevent the disease, which can include diagnostic tests.
Source: US FDA 20May