Can I specify GET URL path parameter in step function?

From the information that you have provided, it seems to me that you are trying to create a step function state machine that uses lambda.

Refer to this documentation it could be what you are looking for: https://docs.aws.amazon.com/step-functions/latest/dg/tutorial-creating-lambda-state-machine.html

If you cannot find what you are looking for in this documentation, please share more about how you are designing your step function, and how you are taking the :parameter value from the input field.