Replacing an Apartment Light Fixture that has a Built-In Switch
Flicking the overhead light might give a voltage transient which starts the fluorescent light. The most you should do in a rental apartment would be to change the bulb. If this is a compact fluorescent with a screw base (and the fixture does not have a build in ballast), you could replace the the fluorescent bulb with an LED. Otherwise ask the management to put in a new fluorescent bulb or you do it. In my youth I got in trouble by messing with fixtures in a rental apartment.

If you are sure that the light is not controlled by a wall switch, I advise you to return the light fixture which has no switch. There is no good way to add a switch.  If you want to change the fixture, get the apartment management to install one of the ceramic bases which has a pull chain. Put an LED bulb in it.

EDIT
The fact that your landlord encourages you to make repairs changes my opinion of your changing the fixture. Until you get one though I would change the bulb. 

I presume you have access to the breakers to shut off the breaker to this circuit. Now you can shop for a fixture which will have a switch. Is this mounted high so that a pull chain is needed or can you reach it so that a mounted switch would work?