Hi there Anna,
Thank you for making a magical stop here at the Disney Parks Moms Panel. I hope you are having a Fantastically Frozen day.
Yes, there are bicycle racks at the Disneyland Resort, they are located in the
Downtown Disney District. Here's some detailed info for you:
"For those Guests who opt to ride their bicycles to the Downtown Disney District, there is a bike rack located on the West end of the Downtown Disney District by ESPN Zone and the Valet drop-off/pick-up area. Because bicycling is prohibited in the Downtown Disney District, Guests may walk their bike upon entering the property to the bike rack."
Just remember to bring and secure your own bike lock, Anna.
I hope this helps and that you have a pixie-dusted time on your next visit. If you have any more questions, please visit me here and let me know how I can help you plan your magical vacation.
Wishing you magic!
~ Lynette