Green’s Dictionary of Slang

blind date n.

[SE colloq. date, an appointment made for sexual/social purposes]

(orig. US) an evening out with someone whom one has never met but who will be introduced by a mutual friend.

[US]W.R. Morse ‘Stanford Expressions’ in AS II:6 275: blind date—assignment to an unknown partner at a dance.
[UK]Wodehouse Mating Season 6: I disliked taking on blind dates.
[UK]N. Dunn Poor Cow 55: I once went on a blind date and then he turned out to be a Persian from Battersea.
[UK]J. Sullivan ‘Go West Young Man’ Only Fools and Horses [TV script] I reckon your best bet is have a blind date.
[UK]Indep. Sport 4 Dec. 16: Blind date. With the bird what gives out the travel information.
Merriam-Webster ‘1920s College Sl.’ [Internet] If he wanted to go to a drag (a dance) […] and had no date, not to worry – take a blind date (a social partner whom one has not met).

In phrases

drag a blind (v.) [drag v.1 (4)]

(US campus) to spend an evening out with someone whom one has never previously met.

[US]DN V 111: To drag a blind [...] To take (or go with) to a dance a girl (or man) one has never seen.
[US]S. Young Encaustics 2: The two were covering some social event [...] The young lady was speaking: ‘And I went. And I had to drag a blind and all that.’.
Merriam-Webster ‘1920s College Sl.’ [Internet] If he wanted to go to a drag (a dance; dragging meant taking a girl to a dance) and had no date, not to worry – take a blind date (a social partner whom one has not met). Combine the two and you could drag a blind – take a blind date to a dance.