ask her out 中her换成she可以吗？

不可以，动词（ask）后面要接人称代词的宾格，所以her可以she不可以,

she的宾格是her
i的宾格是me
he的宾格是him
you的宾格是you
we的宾格是us
they的宾格是them

不可以，动词（ask）后面要接人称代词的宾格，所以her可以she不可以。

No, it can only be "ask HER out." She will never be correct used in this manner, and will actually only make your sentence sound extremely awkward and weird to native English speakers.