Back up iphone without SIM card?

I have two iphone 5 s. One is brand new and the other doesn't charge very well. Can i put my SIM card in the new iphone and still back up my old one without having a sim card in it? And then after my old phone back ups, transfer all the stuff to my new phone?

You will still be able to backup to iCloud with no SIM card as long as you have an active Wi-Fi connection and are signed into iCloud with enough space.