Surprised to find there IS one? Well there is. They divide it into three categories: "Early American Song, 1600-1879," "Tin Pan Alley, 1880 - 1953" and "Rock n' Roll, 1954- present."
Here's the link, they just announced this years' inductees today: http://songhall.org/news/entry/songwriters_hall_of_fame_announces_2013_inductees. Steven Tyler and Joe Perry of Aerosmith, and Mick Johnes and Lou Gramm of Foreigner, are being inducted this year, as well as Holly Knight, JD Souther and Tony Hatch.
Here's the list to CURRENT members: http://songwritershalloffame.com/exhibits/era. Most of the people you expect to be there are there, like Lennon & McCartney, Holland, Dozier & Holland, Bruce, Goffin & King, even the Sherman brothers who wrote every Disney song ever.
What surprised me is who's NOT on the list. John Hiatt. John Prine. Jim Steinman, who wrote "Paradise by the Dashboard Light." Tom Waits. Chrissie Hynde. Justin Hayward from the Moody Blues. Warren Zevon (there's no "Z"s at all!)
I was gonna say Lionel Richie but then I remembered he wrote "We Are the World" so I kicked him off my list.
Anyone you feel should be nominated? List 'em below in the comments.