Currently, Visual Studio Code doesn't provide this specific functionality.
We could vote for this feature at Visual Studio's UserVoice website.
There's already a ticket open for this feature: Paste and auto align code. If you've got an account, you can vote for this feature so it gets more attention. If it has enough attention, Visual Studio Code's developers could take notice of this and maybe develop it.
Current workaround
After pasting the code,
You could use CTRL+E, CTRL+D for windows or ALT+SHIFT+F for mac.
But note that this will reformat the whole document, indenting according to the available rules for the source type.
If you only want this to be applied to the pasted code, select the code after pasting and then use CTRL+E, CTRL+D for windows or ALT+SHIFT+F for mac. Now the indenting/formatting is only applied to the pasted lines.