You can buy Apple Care+ for your new iPhone up to 60days after the purchase:
...
1 . Purchase either AppleCare+ product with your new iPhone.
2 . Or buy it within 60 days of your iPhone purchase:
- On your device (go to Settings > General > About and choose AppleCare+ Coverage Available)
- Online (requires you to verify your serial number and run a remote diagnostic)
- At an Apple Store (inspection of iPhone and proof of purchase are required)
- By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)
For information on how to renew an existing plan, click here.
...
copied from: AppleCare Products - iPhone - Apple