Yes, if you have a title loan, you can still register your car.
Having a title lien on your vehicle doesn't affect your ability to register it since registration and titling are two different things. Let's examine both of these documents and what they're used for.
Many people are under the misconception that a car title and a car registration serve the same purpose or that one can be used in place of the other; however, they are two very different legal documents.
Your vehicle registration proves that your car has been registered with the state and is authorized to be driven on public roads, while your car title shows proof of ownership.
So, your car registration is the thing that: allows you to legally drive your car, you must renew periodically (usually every year), and is managed by your state's Department of Motor Vehicles (DMV); it is completely unrelated to your car's title and your ability to register your vehicle will not be affected if you've chosen to take out a title loan in most states.
When you take out a title loan, a lender places a lien on your car title (which means that they then have a legal claim to your car if you fail to repay) but you can still register your vehicle with a lien. A lien-holder (in this case, the title loan lender) might even be required to be listed on your registration.
So, again, you should have no problem registering your vehicle with an auto title loan! 👍