An air carrier aircraft lost directional control during a slow taxi on an ice covered taxiway; so the Captain shut both engines down as it drifted off the centerline. The aircraft was towed back onto the taxiway.

Narrative

Pushed back from gate with taxi instructions 'hold short D3.' Switched to Ground Control with instructions to' taxi to Sierra deice via taxiway E' Slow taxi; 3-4 knots; both engines running while attempting to join taxiway Echo. Entered a slow left turn when aircraft lost directional control due to taxiway ice. Drifted right of taxiway centerline and slid to a stop. Notified ground; secured engines and called for tug. Aircraft engine was inside blue taxi lights by approximately 4 feet as relayed by ground tug crew. I looked out the R1 Door to confirm position. Informed passengers of the nature of the icing delay. Tug crew pulled forward and easily returned the aircraft to the ramp area which had much better traction. We restarted engines and continued to de-ice area Charlie; then departed Runway 10C. Maintained constant radio contact with PIT ops and phoned Dispatcher of nature of delay. Tiller was unresponsive. Braking nil. I came in the night prior on a stand up. Light freezing rain had frozen to taxiways while on top of older snow deposits.