Not easy.
George I served in the Great Turkish War (1683-99) before he was king. A few conveniently-timed royal deaths can bring him to the throne earlier and he can still command the Hanoverian army while leaving native ministers in charge in England.
The war has to take a significantly different path than OTL to have a siege of Constantinople, however, and for George to lead it. I would guess that the best time would be after the main Turkish army was destroyed at Zenta, and the attack on Constantinople would then be a surprise diversionary attack while the allies' main armies were engaged in Hungary and Serbia. Constantinople is a long way from the main conflict area; there would have to have been a southern thrust by the allies to bring it in range.