I'm going to attempt an answer based on my comments.
"Buzzing" is not a real sitar sound. There are so many differences between these instruments it's hard to say.
There is something called a sitar guitar. I think it was probably popular with some rock players, might have been used on an episode of the Monkey's. If you google the term "sitar guitar" you'll find it. But you probably do NOT want to buy a special guitar.
There is a pedal for this like you want, more than one in fact. There is the Danelectro Sitar Swami, The Karma Suture, and the Electro-Harmonix Ravish Sitar synthesizer pedal. These can get pricey, $200-$300 USD.
These might get you a sitar sound on whatever tune you are playing. However, if you emulate a sitar players technique you would be in better shape! I grew up in an Indian neighborhood in America (I'm not Indian) and both my father and I listen to Sitar music (as well as other Indian instruments). The rapid bending and tremolo while bending, on the right scale, emulate sitar technique pretty nicely. I perform that way for Indian audiences and get comments that it sounds authentic.
Part of "sounding like a sitar" is the style of attack, the note bursts played by sitar players, and most importantly using the modes or scales that are associated with Indian music. This may not be easy for a guitarists as some classical Indian music involves notes that are not in the chromatic scale tuning. But then again so does the Blues. If you can bend a quarter tone her and there, apply some tremolo with it, and do it with some dexterity you can play Indian classical music on your guitar. Carnatic scales are based on 12TET chromatic tuning so using them would work too.