I suspect there is a connection because visual processing ability is necessary in noticing important subtle social cues.
Reading facial expressions is very important to understand others' intentions (Heise, 1985).
Recent research indicates that (1) the human face is a highly sophisticated signaling system for communicating affect, and (2) affect plays a key role in the experience of social organization and in the day-by-day production of culture. This essay suggests that emotional displays—on the face especially—are a primary means of socialization, allowing a neophyte to attain knowledge of the sociocultural system rapidly and efficiently.
Having a visual impairment may yield difficulties in socializing (at least in child in the Autism Spectrum Disorder) (Hellendoorn, et al, 2013):
This study suggests that visual perception may be a mechanism in the development of interpersonal relationships in ASD, which is in accordance with an embodied approach to social cognition.
...and in schizophrenia cases, as per @what comment (Sergi et al, 2006):
Social cognition appears to be a key determinant of functional status in schizophrenia. Using a very basic measure of visual perception, the present study found that social perception mediates the influence of early visual processing on functional status in schizophrenia.
Other indirect consequences may happen due to behavior related to some visual disorder. Vision problems and social skills (note: not a peer-reviewed article):
Vision problems also affect social interaction. Your child might appear awkward, clumsy, or other children may complain that he is invading their personal space, because he has trouble with spatial and body awareness and depth perception. The other children might treat him differently because he has developed coping habits, such as constantly rubbing his eyes, squinting, or tilting his head, or because he often complains of headaches or nausea. He may become distracted while talking or ignore the rhythm of a conversation and other social cues. Children or other parents might unfairly judge this behavior as unmannerly or inconsiderate.
Dealing with difficulty in school, awkwardness in social settings, poor performance in physical activities, and strained relationships with parents is a lot for a child to handle. While children with other learning disabilities may excel in sports or sociability, vision problems interfere more often beyond the classroom. Falling behind academically and being treated differently by peers and adults can lead to low self-esteem and withdrawal.
Yes there is relation, but currently there is no research evidences. its theoretical. As you can observe we at according to situation and its demands. with passage of time our social skills improved and we also learn new skills in such way.