Hello and welcome to planDisney, Emily. I can understand why one would want their visit to the Disneyland Resort to be practically perfect in every way, and how having a handy tool to keep your locks looking lovely would be divine. Let's comb through the details.
While curling irons and other hair tools are not on the
prohibited items list in the park rules, all items taken into the park are subject to search and the decision on what is allowed is ultimately up to the Cast Members at security. Because I can't give you a definitive answer, I would err on the side of caution and leave the curling iron in your car or back in your hotel room if possible. If you decide to try and bring it into the park with you, be prepared that it might not be allowed in and you may need to go back and leave it in your car or hotel room. There unfortunately are no lockers outside of security so this would be your only option.
It sounds like you may be trying to get some unforgettable photos during your visit. If that's the case, I recommend trying to get them done earlier in the day and definitely before a ride on
Big Thunder Mountain Railroad (it is the wildest ride in the wilderness, after all). If that's not possible, might I suggest taking a midday break back in your hotel room where you can freshen up and then head back to the parks camera-ready. A big plus with this option is that you could return right around golden hour for those extra magical shots.
You may also consider taking advantage of
Disney PhotoPass photographers. Some of my favorite memories have been captured by these photographers and everyone gets to be in the picture. You can find a list of PhotoPass locations in the
Disneyland app.
Emily, I'm sorry I don't have a better answer to share with you. I do hope that the information I provided is helpful and gives you an idea of what to expect to help with your planning. Let us know if there's anything else that we can help with. Here's wishing you a magical visit to the Happiest Place on Earth.
Michelle