The "on my phone" part is unnecessary. It doesn't sound natural at all. In the US, most natives would just say, "Call me when you have time" or "Give me a call when you have time." In British English, they might say "phone me" instead of "call me."

In the US, "on my phone" is natural and might even be necessary since there are so many ways to call someone. An alternative would be "call me on Skype", for example. If you want to give a phone number, say "call me at 123-456-7890."

Just a few days ago, I was talking to a person who said that she was going to be out of the office on the day that she needed an answer from me. So she told me to call her on her phone, meaning that I should not call her at the office but rather call her on her personal phone. In a situation like that, where there are several telephones involved, call me on my phone does make sense.

In this sentence, "on" means "using" or "via." So the sentence "Call me on my phone when you have time" means to call the person using their phone number. It's true that a phone is just an object and you cannot use someone else's phone to call them unless they give you permission to do so. Therefore, it's important to clarify whose phone number you are referring to when you ask someone to call you "on" your phone.