Is that her?

Question

or

Is that she?

Answer 1

The correct word is "she."

It's a predicate nominative following the linking verb, "is." Since it means the same as the subject, the word must be the subject pronoun.

That is she.
Is that she?

Answer 2

I thought it was natural to use "her", but I guess it is a common mistake.

Answer 3

you are correct in that it is indeed common, though grammatically incorrect, usage.

Just as are

It's me.
Me too. (usually)