Can I sue a landlord. I was going to rent a home an paid the rent an deposit I got a offer for a home to rent with option to buy so never moved into the home nor did I sign any type of lease nor agreement I only asked for deposit back an she refuses an said she would give it back if I found a new renter. Can I sue for the full amount back?

Depending on rental laws where you live you should be able to get something back. But not all. You have to understand that the deposit alone represents a contract. A contract of intent. This person that you gave the deposit to removed the unit from the rental based on promises you made. They are entitled to expenses for you breaking that contract.

If this was a month to month rental, you will owe for the first month. If they move someone in, prior to the end of first month, you will only owe partial month.
This is a basis and general rule, but may vary on your exact locaton

Anyone can sue over anything. The correct question is will you win. The likelihood in this case is that you won't. The purpose of a deposit is to hold something pending completion of the transaction. Unless you have some documentation that the deposit was refundable, the landlord is within their right to hold onto it. They probably took the unit off the market based on your commitment to rent it. Now they have to go back to finding a tenant.