As several buried answers have pointed out, this is possible now. Here's how, with screenshots:

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Click on the terminal name in the side panel and select "Move Terminal Into Editor Area". This will move the terminal into a new editor tab.

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If you have multiple terminals open, you'll need to right click on it in the list of open terminals instead.

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Right click on the newly-created terminal tab and select "Move Into New Window".

Per the docs:

Mac OS X

1. Download Visual Studio Code for Mac OS X.
2. Double-click on VSCode-osx.zip to expand the contents.
3. Drag Visual Studio Code.app to the Applications folder, making it available in the Launchpad.
4. Add VS Code to your Dock by right-clicking on the icon and choosing Options, Keep in Dock.

Tip: If you want to run VS Code from the terminal, append the following to your ~/.bash_profile file (~/.zshrc in case you use zsh).

code () { VSCODE_CWD="$PWD" open -n -b "com.microsoft.VSCode" --args $* ;}

Now, you can simply type code . in any folder to start editing files in that folder.

Tip: You can also add it to VS Code Insiders build by changing "com.microsoft.VSCodeInsiders". Also if you don't to type the whole word code, just change it to c.

Linux

1. Download Visual Studio Code for Linux.
2. Make a new folder and extract VSCode-linux-x64.zip inside that folder.
3. Double click on Code to run Visual Studio Code.

Tip: If you want to run VS Code from the terminal, create the following link substituting /path/to/vscode/Code with the absolute path to the Code executable

sudo ln -s /path/to/vscode/Code /usr/local/bin/code

Now, you can simply type code . in any folder to start editing files in that folder.