Yes you can get bicycles, there are various shacks offering the cycles for Rs 100-200 per day, depending on the type of cycle you want.
You just have to submit an identity card and your'e ready to enjoy the ride.
Depending upon the type of bicycle you want, there are so many vendors where you can hire bike/bicycle/scooty on rent. You can checkout: Vijay Arya Scooter Rental (Thennanjalai Road), Pondy Bike Rent (Chellan Nagar Main Rd) etc. Please search more options as per your convenience on Google.