I have an iphone and my son is getting an iphone, but we only have one computer?

Can i plug his iphone into my itunes account?

You can actually make him his own iTunes account! Just log out of your account & plug his phone in.

Yes, it'll give him access to your account though (I.e.apps, music, contacts, etc.)

Also if you have a credit card or gift card balance on your account he can use it

Yes, one iTunes on one computer can be synced to multiple iOS devices, such as iPads, iPods, iPhones. You can also use your account on his phone.

ITunes can support at least 3 devices at once. I've had an iPod Touch 5th gen, an iPhone 5 and an iPod (2004) all connected by usb on an HP Probook at once.