I think this might be is a trifle matter but since it leaves with some doubt, please answer this.
In the post, their is used to refer to his or her and used in part to avoid mentioning the gender; then wouldn't it be more appropriate to make the sentence to reflect that like this?
"If anyone calls, ask for their number so I can call that person back"
As I said, the their/them version is what is commonly said. Once you accept the use of 'their' to avoid the his/her problem, 'them' seems to follow naturally.
Your version certainly isn't wrong, but it sounds stilted.
Finally, I don't want to leave you with the impression that there is anything terribly wrong with saying If anyone calls, ask for
They are all acceptable. The problem of their vs. his/heris one that English does not have a great solution for, so some of these make me feel slightly uneasy. But I have a cup of tea, and then I don't feel uneasy anymore.