Would you like to swing on a star was a Top Ten hit for which singer? "Swinging on a Star" won the Academy Award for Best Original Song in when it was featured in Going My Way, and sung by that ol' crooner, Bing Crosby! Lyrics to Swinging On A Star by Frank Sinatra: Would you like to swing on a star? / Carry moonbeams home in a jar? / And be better off than. Lyrics to 'Swinging On A Star' by Bing Crosby. Would you like to swing on a star / Carry moonbeams home in a jar / And be better off than you are / Or would you.