In the user entity, there are 2 fields: a single-valued field_department_text A (a text field) and a multi-valued term reference field_department B. Now, I need to use Rules to append A's value to B when a user was created. I tried, but failed.
Looks like you could just use the "add to list" Rules Action.
For multi value fields you should not use "Set a data value" (which is possibly what you've tried, a common mistake when using Rules for such fields).
Refer to the answer to "How to set multiple values to an unlimited Term Refence field with Rules" for "some" more details ...