Sort of.

During the Balkan Wars, Bulgaria was engaged in a protracted fight against the Ottoman army at Çatalca (transcribed at the time as Chataldja). However, you might quibble as to whether this constitutes a "siege of Istanbul" on two points:

1. This encounter is usually described as a battle rather than a siege, although the Çatalca Lines were indeed a series of fortifications that Bulgaria ultimately failed to take.
2. Çatalca is not exactly Istanbul; it's more like the outskirts of the city, although today Çatalca is part of the Municipality of Istanbul and it was part of the Province (vilayet) of Istanbul in 1913.