If you search YouTube by that title you'll find a Stringbean/Grandpa Jones/Ronni Stoneman et al. group performance of it. However, the lyrics don't match the original, having been adapted over the years. There are two revival band performances as well, one under this title and one with the title spelled "Tickling."

But you can find a recording of the original by its composer!! Read on.

The song was written by Silas Leachman (1859-1936), a Chicago politician(1) and vaudeville performer responsible for creating or adapting some early classics, including "Whoa Dar Mule" (1901), "Good Morning Carrie" (1902), "Mr. Johnson Don't Get Gay," and "Sit Down."

Several sites offer downloads of Leachman singing "Quit That Ticklin' Me" — The best possibility is probably Internet Archive at:

http://archive.org/details/LittleSilasLeachman-11-16

Happy listening. Bob