Why is this wrong - "an gcuirfidh tú glaoch orainn inniu"
That’s probably closer to “Will you place a call to us today?”.
That's a pretty standard way of saying it though don't you think?
The exercises here tend to be written to prefer more literal translations, since the courses here are aimed towards beginning students.
"An gcuirfidh glaoch tú orainn inniu?" was my answer, as well. I think it should be acceptable, especially given that Duo has used the "cuir glaoch ar" construction for the present tense of "to call" in earlier lessons.
It's not acceptable because the subject comes after the verb, and the verb is cuir, not cuir glaoch.
glaoch is a noun, and would be the grammatical subject in your construction.
Nach bhfuill an nglaofaidh sibh orainn? ceart chomh maith?
I'd flag it.