to have or have got in the sense of own or have relevance to a person (have sisters, for example):
There are two different forms: have and have got = same thing.
- Have you got a car? The auxiliary is have. So have I.
- Do you have a car? The auxiliary is do. So do I.
So: "So have I." for have got and "So do I." for have.
The answer depends on the question you were asked and how it was asked: was it asked with have or have got (which mean the same thing, I cannot stress enough). The only difference is that have got is usually a spoken form.
When one teaches English, one deals with this all the time.
Please note: Usually, one tends to answer a question as it was posed.
So, if the person asks you: Do you have an X? The most likely auxiliary will be "do". Whereas if a person ask you: Have you got an X, the most likely answer is with "have".
Please note: also, it used to be common to hear: Have you money? And the auxiliary there is have: Yes, I have. This usage is quite rare in AmE. But I hear it quite a bit on British drama series, etc.