Update 2022-12-27
On the Source Control tab (Ctrl+⇧+G or ^+⌘+G on Mac), press ⃛ to access Git commands dropdown menu:
Switch to the branch to push – Branch > Create Branch OR Checkout to... > ➕ Create New Branch

Press the Commit & Push button (if not visible, press ⌄ under the Message text box)
two popups will show up for you to confirm staging, committing and pushing of your changes to this new branch

Alternative using only menu options:
- Switch to the branch to push – Branch > Create Branch OR Checkout to... > ➕ Create New Branch
- Stage your changes – ➕ button above the files list OR Changes > Stage All Changes (several Git: options available)
- Commit your changes – ✓ top left button OR Commit
- Push the new branch: Branch > Publish Branch (or just use the Push option and press OK in the popup)
All above options can be accessed through commands F1 (Mac: fn+F1 or ⇧+⌘+P) and typing git [command], e.g. "git checkout".
For previous versions, check this answer's timeline.
git push origin brnach_name?