The disturbing incident happened in Skipton on Tuesday when the girl was walking home from Greatwood Primary School.
Dramatic video shows boat catching fire on canal at SkiptonThe 11-year-old, who was with a friend, was approached by a man next to the Cock and Bottle pub on Swadford Street just after 3.30pm.
140 new homes to be built in SkiptonHe said 'hi' to the pair and passed her a piece of paper with his number written on it, before saying 'phone me'. He then crossed the road and left the scene.
The girl went to her grandfather's house nearby and told him what had happened.
The man is described as black, aged in his 30s, clean shaven, approximately 5ft10 tall, of slim build with dark, short Afro hair. He was wearing dark clothing and had a backpack.
Police are asking for anyone who may have witnessed the incident, or who saw a man of the above description in the area at the time, to get in touch.
Anyone with any information is asked to contact North Yorkshire Police on 101 and pass information to the Force Control Room, quoting reference number 12180109296.