The correct answer is 'I'm going to answer.'
Explanation:
The sentence 'The phone is ringing' indicates an action that is happening right now. The appropriate tense to use when we have an ongoing situation is the near future, and in such a case we can use 'I'm going to answer.' The other possible answer is 'I will answer'. However, 'I'm going to answer' is used when you already made a plan/decision to answer the phone, or when the action is imminent. Therefore, since the phone is ringing right now, and the person likely is going to pick up the phone, this tense is better suited. 'I'm answering' would be the correct answer if you were already in the process of answering the phone at the moment of speaking.
Therefore, the best option here is 'I'm going to answer'.