To obtain a "handicapped" license for a motorcycle, you will need to get a disabled parking placard or plate from your state's Department of Motor Vehicles (DMV), not a specific "handicapped" driver's license. This involves a doctor certifying your disability, a medical condition that prevents you from walking short distances or requires specific accommodation. Once approved, you will receive a placard or plate that can be used for your motorcycle, allowing you to use designated disabled parking spaces.
I believe a states support this but could be wrong.