Yes, you can! And you can also talk with your friends using voice chat.
The Friends button is located in the bottom right corner, next to chat and settings. Tap it and go to:
- Add friend - to search for friends by the username
- Recent players - to go through players you played with during your previous few matches
Finally, tap on the blue Add friend button to send a friend request. The player you chose to add as a friend will move to the Pending tab until they respond to your request. Similarly, you will find requests from other players under the Requests tab.