I can also read this in your screen-shot:
Can't use Subversion command line client: svn
Probably the path to Subversion executable is wrong. Fix it.
You're apparently assuming that your IDE works on top of TortoiseSVN and that isn't the case. You need to install the Subversion command-line client. TortoiseSVN actually bundles it, but it's an optional component.
In more general terms, Android Studio is based on IntelliJ IDEA, which is a Java-powered IDE that bundles its own Subversion client. Most likely, you are using latest TortoiseSVN and it created a Subversion 1.8 working copy. Most Java-based IDEs do not support 1.8 yet. Perhaps it allows to use the command-line client as workaround.
Solutions:
- Get an older TortoiseSVN
- Wait for a newer Android Studio
- Install the command-line client as the program suggests
Edit: apparently, it isn't entirely clear how to install the command-line client packed with TortoiseSVN. Here's a screen-shot from the installation wizard I found in Google images (it shouldn't be very different from latest release):

You need to click on the little rectangle with the red cross to the left of "command line client tools" and select "This component will be available" (or a similar text). Then click Next until you're done.