David Turner was filmed by his nephew Blade James attempting the shot while surrounded by encouraging loved ones.
David was directed by his nephew – who was stood a little to the side of the net – to aim the shot towards his voice.
And after queuing the shot up, the man calmly threw the ball into the air.
The ball bounces off the back post and falls directly into the net.
Despite being unable to see his attempt, David was informed of his success by the eruption of celebrating witnesses.
Blade can be heard shouting: “He made it, he made it.”
Despite David’s condition being so far unknown, on Twitter, his nephew told one viewer that he lost his vision five to six years ago.
The video – believed to have been filmed in Texas, US – has been seen more than 10million times since being posted to Twitter.
It was captioned: “My uncle blind y’all, and made a free throw on his first try.”
Thousands of people have shared their joy after watching the video, with many congratulating David.
One viewer said: “Thank you for sharing. I needed a happy lift.”
A second said: “This is beautiful.”
Others called for the man to be signed by the NBA.
It is not the only heartwarming video to have emerged in recent weeks.
A four-year-old was filmed ringing the “clear-of-cancer” bell earlier this year.