Before you do anything else, it is important for you to talk to your father about his behavior, and it's effect on you. He may be elderly and unhappy, but
that does not give him the right to abuse you. Unless he is suffering from some type of mental illness, there is absolutely no excuse for his behavior, and you should not tolerate it.
You also have the right to set some parameters around your contact with him. Arrange to call him every few days at a specific hour that is convenient for both of you, and stick to this schedule. Make it clear that as much as you care about him, you also have work and personal obligations that need your attention. You should also make it clear that you won't stay on the phone if he badgers or yells at you. Having said that, it sounds as if your father is in some distress, and needs help, whether he is willing to accept it or not. We consulted several experts, who agreed that your father's behavior could indicate some kind of serious problem, since you said that he is not normally prone to angry outbursts. Your father's distress could be caused at least in part by depression, illness, or dementia, and treatment is likely to bring him -- and you -- some relief. Contact your father's physician and explain what is going on, and make sure he goes in for an examination soon.
It sounds as if you are caring for your parents from a distance. If so, you may want to ask your care manager to get more involved, at least until you get the situation stabilized. She should be able to give you some insight into your father's condition, and also to put you in touch with the appropriate experts and resources.
Best of luck and keep in touch.