are two answers, really, because the first recording of an electric blues
guitar was for demonstration purposes only. It was during the days when Rickenbacker
was testing out the first electric guitar which guitar geeks (sorry, aficionados)
will know was nicknamed the frying pan.

 In 1932, a 28-year old white band leader
and Hawaiian guitarist called Gage Brewer, from Wichita, Kansas, recorded Eddie
Green’s 1918 blues composition, ‘A Good Man is Hard to Find’, as a demonstrator
record for the new electric guitar company.
Eddie Durham
While not a commercial
recording, this is thought to be the first time anyone had played an electric
guitar publicly. Brewer later took the new electric guitar on the road with
his band; and broadcast the Rickenbacker’s exciting new sound over local radio.
Probably the first
blues-oriented electric guitar ever recorded commercially was by the virtuoso
trombonist and guitarist, Eddie Durham. Of African American, Irish, Mohawk and
Cherokee Indian descent, Eddie Durham was from San Marcos, a place so deep in
the heart of Texas, he spoke only Spanish as a youngster. In September 1935, when Eddie was 29, he recorded some bluesy
electric guitar licks with amplification he had rigged up himself, on the swing
era tune, ‘Hittin’ The Bottle’, for the black bandleader, Jimmie Lunceford.
Eddie Durham would
later teach Charlie Christian how to play the electric guitar and is also
credited with recording the world’s first electric guitar jazz solo on Lester
Young’s Kansas City Five sessions in 1938. Eddie Durham co-wrote Count Basie’s
‘Topsy’, arranged Glenn Millar’s iconic Second World War anthem, ‘In The Mood’,
worked with everyone from Billie
Holiday and Cab Calloway to Artie Shaw and Earl Hines.

Listen to Eddie Durham in 1935 on the link below. His electric guitar comes in after 48 seconds.