Hey there Marcus,
Welcome to planDisney and thanks so much for your question!
I love this question almost as much as I love pizza. According to the
Disneyland Resort Rules and Regulations page, you are allowed to bring outside food and non-alcoholic beverages into the Disneyland Resort parks. Guests (including me!) do this all the time.
Though I will add that ultimately you will need to follow the guidance of the Cast Members at the screening stations as I could certainly see situations where this could not be allowed. Since I don't know exactly what you're wanting to bring in or how you're planning on bringing it, I can't give you a definitive and unequivocal "yes, you're 100% good to go" but I can detail out the guardrails and how I would suggest bringing it in!
The main restrictions to know are that you can't bring in glass containers, hard-sided coolers, or alcoholic beverages. Therefore, my suggestion would be to pack your pizza into storage bags within a lunchbox as that will be the best way to transport it with you until you're ready to eat it.
Of course, if you'd rather not lug a pizza box through the parks all morning, the Disneyland Resort has no shortage of great dining options inside. My family is always tempted by the Monte Cristo sandwich over at the
Blue Bayou Restaurant, and my kids are never going to turn down a corn dog from the
Little Red Wagon in Main Street, U.S.A. But bringing your own food is a totally valid way to stretch the budget, and plenty of guests do it every day.
Thanks again for stopping by planDisney, Marcus. I hope you have an incredible visit to the Happiest Place on Earth!
Have a Magical Day,
Greg