There are a few other ways you can hang curtains in a rental that won't require drilling or cause damage:
Spring tension Rods or Twist-and-Fit Rods
Spring tension rods or twist-and-fit rods are affordable and easily adjustable options that can fit most windows. They come in different sizes and you can fit them inside the window frame.
Pleated Paper Blinds
If you need an extra light-filtering layer on your windows, try pleated paper blinds. You can trim them to fit your window. No need to pull out the tools…just peel and stick! You can add these to your windows and then add a rod to layer a set of curtains over them.