I wasn't able to figure out this way, however after a bit of diggin on the app I've found another way.

Once you open the Rover app, open the side bar by clicking the three bars in the top left corner. Scroll down until you see "profile" and click that. Then, press the pencil button in the top right corner. This should take you to account info. You're going to want ro press "Update". Once you've done this, continue to the "Basic Info" tab and scroll down until you see an option to upload a new photo. This option isn't shown in the "Photos" tab along with your cover photo and additional pictures which I found very strange.

I hope this helps!