"To register you moped, you must first get a Texas Safety Inspection Sticker and then take the following information to the Travis County Tax Assessor-Collector's Office:
bill of sale from the seller;
vehicle identification number;
proof of insurance;
driver license; and
* the required registration fees.
Please contact the Travis County Tax Office at (512) 854-9473 to inquire about additional filing instructions, the required registration fees and the address of the tax office located nearest to you.
Thank you for your inquiry."
from this person:
Terry Sue Stabeno
Texas Department of Motor Vehicles
VTR Customer Services Representative II
Correspondence Services Branch
They also gave me instruction on how to get a title but told me that: "You will not need it to register your moped. You would only need it if you were wanting a title."