Dogan Arslan, 47, is accused of staring at Ms Sturgeon and her Pollokshaws Road office from a parked car outside.
Arslan, from Battlefield, in Glasgow's South Side, yesterday failed to turn up at court.
He is alleged to have carried out the offence between October and December 2012.
It is claimed that he "engaged in a course of conduct" which caused people in the office, including the SNP politician "fear and alarm".
He is said to have "repeatedly loitered within a parked motor vehicle in the vicinity of the office premises" and stared at the offices and Miss Sturgeon.
His case called for a procedural hearing at Glasgow Sheriff Court but Arslan was not present and a warrant to apprehend him was granted by sheriff Brian Adair.