On Broadway, Parker appeared in
Rainbow (1928),
Spring is Here (1929),
Heads Up! (1929),
Girl Crazy (1930),
Red, Hot and Blue (1936),
Are You with It? (1945),
The Front Page (1946),
Ankles Aweigh (1955),
Mr. Wonderful (1956), and
A Funny Thing Happened on the Way to the Forum (1972). On television, Parker appeared on one episode of the television series
Gidget in 1966 as Mr. Socrates, the crusty proprietor of The Shaggy Dog, a hamburger restaurant that was a hangout for teenagers. Parker appeared in the television series
F Troop in 1966, "The Ballot of Corporal Agarn" as George C Bragan. Parker's character is a mayoral candidate from Corporal Agarn's hometown in New Jersey, and he travels West to get Corporal Agarn's vote since the election was tied and Agarn's absentee ballot is needed to break the tie. From 1966-1971, he appeared in 63 episodes of
That Girl as Lew Marie, the father of
Marlo Thomas's character, Ann Marie. Parker also appeared in episodes of
The Lucy Show and ''
Here's Lucy''. ==Personal life/death==