会 has the meaning of "can, be able to, will". In this sentence, 会=will 打电话is a phrase, means "call sb., make a phonecall to sb." Other similar examples of 会: 明天他会来吗？今晚不会下雨。

The sentence can be segmented as follows: 我 I 会 will 打电话 make a phone call 给 to 他 him While 给 generally means "give", it works like "to" to indicate the recipient in the following fixed expressions: 打电话给他(call him by phone") 写信给他(write him a letter) 寄信给他(send him a letter) 发电邮给他(send him an email) 发短讯给他(text him) 发传真给他(fax him)

"會" means "will" "打" usually means "to heat" "打電話" is a collocation, means "call"

汉语的“会”不能等同于will。”会“的这种助动词用法来自”能“的意思，而will是来自”愿意“。

会打 means making a promise.