While there isn't a simple, automated metric that will tell you how many people have signed up for your app within a certain timeframe, you can do this by looking at your app data for the User data type.
To see how many people signed up (aka created an account) within a certain timeframe, you can create a new data view and filter the data to display User entries that were created within that particular timeframe.
Keep in mind that this approach will only work if you're using the Sign the user up action or the Signup/login with a social network action because these actions save users to the database.
