Unfortunately the simple answer is no. The iPhones 4's battery has a different voltage and the connector is slightly different. If you need a new battery you can get one from here,
that will work no problem in your phone.
Hope this helps.
Replace that dying battery or carry an extra for backup power! 3.7 V, 5.3 Whr, 1430 mAh. Compatible with all iPhone 4S models. — 50+ available at 29.95 each.