Hi there Amanda,
Welcome to planDisney and thanks so much for your question!
I'm happy to share that you certainly can bring a backpack in with you on your visit to the Disneyland Resort, though there are some guidelines to be aware of.
First, know that it will be screened when you enter the Disneyland Resort area by the security checkpoint and they will be looking to make sure the bag and its content adhere to the
Park Rules and Regulations. Specifically, you'll want to make sure that the bag is no larger than 24" long x 15" wide x 18" high and doesn't contain anything in the prohibited items list on that same page.
My wife and I have two young kids so we almost always bring in a backpack of some sort to carry things we need into the parks like snacks, water bottles, and a spare set of clothes. Keep in mind that in many attractions, you'll need to take your backpack off while you ride. Some attractions have mesh storage areas while others you can just keep your backpack at your feet.
If you need a break from carrying your backpack around during the day, you can also
rent a locker. These are located near the entrances of each park, come in various sizes, and are available on a first come, first served basis.
Thanks again for your question, Amanda! I hope you have a wonderful time on your visit to the Happiest Place on Earth.
Have a Magical Day,
Greg