Well, considering how expensive those phones are, I can't really blame your mom for not "giving" you one. When you become and adult, things aren't just given to you. Perhaps you could talk to your mom, and tell her you will find a job, or some chores that might help "pay" for the phone yourself. 1. Help pay for it, by getting a job or doing chores around the house. 2. Prove to her you are responsible. 3. Try settling for something cheaper.
First, you need to have a discussion with your mom about the advantages and disadvantages of having the iPhone. Make sure that you parents are in good mood and that your grades are up in school and you respect and obey your mom fully. Then, you can now tell her that you want to have an iPhone. Wait for her response and don't nag her as this might annoy her. If some weeks pass without getting you one, talk to her again and remind her then be patient.