It's likely you're thinking of a popular radio show called "The American Radio Digest" which began in 1939 and featured "The Funnies" segment. This segment would often feature a well-known actor or personality reading comic strips over the air.
However, FDR was never involved with this show or any other similar radio program.
It's possible the confusion arose from the fact that FDR was a strong supporter of radio as a medium and often used it to connect with the American public during his presidency.