The eponymous award recognised the singer's "artistic talent and influence".
Swift told the audience: "If they had chosen someone else to give the Taylor Swift Award to, I'd be kind of bummed about it."
It is only the second time the BMI has created an award in an artist's name. The first was Michael Jackson in 1990.
The BMI - whose full name is Broadcast Music, Inc - keeps track of the songs played on radio and television, and collects royalties on behalf of writers and publishers.
Now in their 64th year, the BMI awards honour the writers and publishers of the most-performed pop songs during the past 12 months.
Swift had four of the year's most-performed songs, which earned her the "pop songwriter of the year" prize.
The singles - Bad Blood, Blank Space, Style and Wildest Dreams - all featured on her chart-topping album, 1989.
The star confessed she was constantly compelled to write music.
"My favourite part is when I'm in the middle of a conversation with my friends and my eyes glaze over and I awkwardly run over to a corner," she said.
"I have to explain to them that I have this issue called: 'I love song-writing so much that it interrupts my daily life'."
BMI vice president Barbara Cane explained the decision to create an award in Swift's honour, saying she had "transformed pop culture", not just through music but by supporting other artists and challenging streaming services to pay musicians fairly.
"She has had a profound impact, not only musically, but also through her personal conviction and commitment to create a standard that values and respects music for everyone," said Cane.
"We felt it appropriate to award Taylor with an honour that is as unique and special as she is."
The BMI also honoured Uptown Funk as its Pop Song of the Year, while Barry Mann and Cynthia Weil, the song-writing team behind classic hits including You've Lost That Lovin' Feeling, On Broadway and Just Once, were presented with the BMI Icon Award.
Many other artists were recognised for writing airplay hits, including Jason Derulo (Trumpets), Flo Rida (Somebody), and Rachel Platten (Fight Song).
Pop star Taylor Swift has been presented with a prize in her own name at the BMI pop awards in Los Angeles.