American plug ≠ European plug
In the United States the voltage is different as in Europe, 110-120V 60Hz instead of 220-230V 50Hz. For most European electrical equipment this is not a problem. You can perfectly use your own charger for you smartphone or tablet.
But... you will have to bring a converter to plug your charger in an American socket. In Europe we use type C, E and F plugs with round pins. In the USA type A and B plugs with flat pins are used.
In the USA it can be hard to find a converter, so it's best to buy one (or more) before your trip. We say 'or more' because you want to charge your smartphone while you write a tripreport on your laptop.