How can I clear the terminal in Visual Studio Code?

Use Ctrl+K. This goes clean your console in Visual Studio Code.

Per comments, in later versions of VSCode (1.29 and above) this shortcut is missing / needs to be created manually.

• Navigate: File > Preferences > Keyboard Shortcuts
• search for workbench.action.terminal.clear
• If it has no mapping or you wish to change the mapping, continue; otherwise note & use the existing mapping
• Double click on this entry & you'll be prompted for a key binding. Hold CTRL and tap K. Ctrl + K should now be listed. Press enter to save this mapping
• Right click the entry and select Change when expression. Type terminalFocus then press enter.
• That's it. Now, when the terminal is in focus and you press Ctrl+K you'll get the behaviour you'd have expected to get from running clear/cls.

Ctrl + Shift + P and select Terminal:clear