You can do it with a rule like this:
MyObject.ModifiedUserID = LoggedInSystemUser.ID
Consider replacing the user ID attribute on the object with a reference attribute to the user object. This way you will get access to all attributes of the user object representing the user who modified the object - not just the ID. The rule would then look like this:
MyObject.ModifiedBy = LoggedInSystemUser
If you know that the modifying user will always be represented by a specific object, for example Employee, you can make the reference attribute on the object to be of type Employee and display relevant attributes like Name, Job Title, etc. The rule would then look like this:
MyObject.ModifiedBy = LoggedInEmployee