Definitely possible to have a "form" in ArcMap that prompts you to type in values... are you looking to add new records to a table? Or are you looking to add new points or polygons?
If you have the correct attributes/domains, and have an edit session open, the "form" is the attributes window...
IF you're looking to append data to a table, you could write a script to append a row to the table, and attach the script to a tool.
If you're not talking about doing this in Desktop, but rather in a web-application...
It really depends on you're purpose etc.