If your Iphone doesn't have enough storage to backup files then you should be able to connect your Iphone to your computer and move the files over to a external Hard Drive or even the computers hard drive.
If you have online storage you could back up your data from your Iphone to online storage or to the cloud.
You can also get a Micro SD card adapter to plug into your Iphone and backup your Iphone data to the Micro SD card.