Can I use an indoor extension cord outdoors with electrical tape?

No. Indoor extension cords are not built to handle moisture, temperature swings, or UV exposure. Wrapping the connection in electrical tape does nothing to seal the cord itself — water will find its way in through cracks in the insulation, at the plug, or along the length of the wire. Once moisture hits the copper, you’re asking for a short, a shock, or a fire. Buy a cord rated for outdoor use instead.