Yes, you can tell what transmission you have by the VIN. The VIN is a 17-digit code that is unique to your vehicle. It is located on the driver's side of the dashboard, near the windshield.
The first 8 digits of the VIN are used to identify the engine and transmission. The ninth digit is used to identify the model year. The tenth digit identifies the plant where the vehicle was assembled. Digits 11 through 17 are reserved for individual serial numbers.
To decode your VIN, look for a chart in your owner's manual or online that will give you the meaning of each digit in your particular VIN.