They are both correct. When I was at school in the 1950s, 'have got' was regarded as very informal; we were taught to use only 'have'. 'Have got' is still perhaps better avoided in formal writing but, in BrE at least, it is far more commonly used in speech and informal writing than 'have'.
I am speaking only 'have' with the meaning of 'possession' (in a very loose sense of the word). When 'have' has a more dynamic meaning (similar to 'take', 'experience', 'eat', etc), then 'have got' is not possible:
I have (got) a shower in my hotel room. It's very modern.
gota shower every morning before breakfast.