Of course, you can.
To add a player as a friend, ask your friend for their Player ID (the code that can be found on your friend's profile).
When you have your friend's ID, enter the new Friends section (accessible through a shortcut on the game's top bar) and enter the "Add Friends" subsection.
Once here, search for your friend's ID and send them a friend request. If the other player accepts it, they will appear in your Friends List. Note that there is a limit of 100 friends per player.