@mmeyerBV83N
Is there a way to create a text parameter in a Revit Family?
Yes, this is straightforward but you will need to decide whether to make it a type or instance parameter. Here is a link to the Revit help concerning the creation of a parameter in a revit family:
Create Family Parameters
For example, I'm working on a door family and would like to have the a lockset option with a dropdown option: entry, storeroom, classroom, privacy, and passage.
As the same door type could be used for different lockset options, I would suggest you create an instance parameter for the 5 options.
You also mention a dropdown functionality which I presume means you want to control/limit the choices to those options. @ToanDN recommendation of a key schedule bypasses the creation of a parameter in the family file and will allow you to setup the initial 5 options. This setup will reside in your Revit project file though and has the advantage of being easily customizable per project.
Create a Key Schedule
This said, if your want to limit the choices to only those 5 options in the Door family, there are ways of achieving this thru a complex set of parameters. The disadvantage of this method is that each Door family you create will have to repeat the same complex set of parameters.
Hope this helps,
-luc