A Delta Airlines Boeing 757-200, registration N6713Y performing flight DL-1088 from Minneapolis,MN to Anchorage,AK (USA) with 206 people on board, was enroute at FL360 about 50nm westnorthwest of Whitehorse,YT (Canada) when the crew received a low pressure indication for the crew oxygen system. The captain tested his oxygen mask and found it was not working. The crew worked the related checklist and initiated a diversion to Whitehorse. The aircraft landed safely in Whitehorse. A replacement Boeing 757-200 registration N538US was dispatched to Whitehorse and reached Anchorage with a delay of 21 hours. The Canadian TSB reported maintenance observed a leak on the captain's oxygen mask hose connection and replaced the mask and storage box. In addition the crew oxygen regulator was replaced, too. The occurrence aircraft was able to position back to Minneapolis about 15 hours after landing.