The correct answer is: C. I’ll ask her.
The sentence is about a request to ask someone to do something. The speaker is asking the listener to ask Ann to phone them. The listener agrees to do this, and says “I’ll ask her.” This is the most natural and idiomatic way to complete the sentence.
The other options are not as natural or idiomatic. Option A, “I ask her,” is grammatically correct, but it sounds like the speaker is asking the listener to ask Ann to phone them right now. Option B, “I’m going to ask her,” is also grammatically correct, but it sounds like the speaker is planning to ask Ann to phone them in the future. Option D, “Asked her,” is grammatically incorrect, because it uses the past tense form of the verb “ask” to refer to a future event.
In conclusion, the correct answer is: C. I’ll ask her.