Question: Can one fulfill the requirement of visiting the sick over the phone?
Answer: According to Chazal HaShem visited Avraham on the third day after his Brit Milah and from there we learn of the guidelines of visiting the sick.
In Nedarim 40 is a story about one of Rabbi Akiva’s students who was sick and there was no one to visit him. Rabbi Akiva came and swept the student’s room for him. The student told the Rabbi “Rabbi, you brought me back to life. When the room was dirty I was like a dead man. After this incident Rabbi Akiva returned to the Beit Midrash and declared that whoever does not visit the sick it is as if he has killed them.
Rabbi Moshe Feinstein deduces from this Gemara that the main part of the mitzvah is to respect the ill and actually visit them in their residence. His conclusion is that you can visit the sick by making a phone call, but do not fulfill the obligation ideally because certain things are lacking. When a sick person is visited in person it gives him greater relief than a phone call. In addition, when a person sees the ill and their illness one understands more what they are davening for and will pray with greater kavana(intention). Rabbi Ovadya Yosef agrees with this conclusion and adds that, according to the Kabala, the prayer after seeing the illness is more accepted when it is said next to the sick person.
Conclusion: One can fulfill the requirement of visiting the sick over the phone, but it is better to visit in person.