Yes you can bring a portable charger on the plane in your carry on luggage.
It's a good idea to bring a portable charger on the plane for your phone, tablet etc so that you can always keep your phone, tablet etc charged up.
Portable battery banks are also allowed in your carry on luggage.
Basically according to the TSA all airlines will allow some batteries or portable chargers on the plane in carry on luggage or even in your checked baggage.
The only batteries that are not allowed on the plane either carry on or in checked baggage is batteries such as car batteries, lawn mower batteries or any other large batteries.
Other battery types are allowed on the plane in both carry on luggage or checked luggage.