Many people commented that they wish there was a shortcut for it. I figured a way to create a shortcut for that from another answer on AskDifferent which I cannot find the link to. This is how:

Open System Preferences;
Go to 'Keyboard' settings;
Go to 'Shortcuts' tab;
In the left pane, select 'App Shortcuts';
In this section you can add app specific shortcuts, as well as shortcuts that you want available for all apps.
Click on the '+' sign below right pane to add a new shortcut;
A new drop down will open. In this drop-down:
In the 'Application:' keep it for 'All Applications';
In the 'Menu Title:' type 'Tile Window to Right of Screen'. Better that you copy-paste it because it has to match letter by letter;
In the 'Keyboard Shortcut:' press the keys you want to use as shortcut for tiling an application window to the right. On my machine, I've set† it to ⎇⌘→.
Repeat the same for tiling to left by putting 'Tile Window to Left of Screen' in the 'Menu Title:' and adding your desired keys for left-tiling shortcut.