Dogan Arslan, 47, is accused of staring at her and her Pollokshaws Road office from a parked car outside.
Arslan, from Battlefield, in Glasgow's south side, is alleged to have carried out the offence between October and December 2012.
It is alleged that he "engaged in course of conduct" which caused people in the office, including SNP politician Nicola Sturgeon "fear and alarm".
It is claimed Arslan "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.