To achieve this in Visual Studio Code, you have to edit keybindings.json. Use the Command Palette with CTRL+SHIFT+P, enter "Preferences: Open Keyboard Shortcuts (JSON)", and hit Enter.

Then add to the end of the file:

[
    // ...
    {
        "key": "ctrl+tab",
        "command": "workbench.action.nextEditor"
    },
    {
        "key": "ctrl+shift+tab",
        "command": "workbench.action.previousEditor"
    }
]

Alternatively, to only cycle through tabs of the current window/split view, you can use:

[
    {
        "key": "ctrl+tab",
        "command": "workbench.action.nextEditorInGroup"
    },
    {
        "key": "ctrl+shift+tab",
        "command": "workbench.action.previousEditorInGroup"
    }
]