score:11
According to Google Books the book "Respectfully Quoted: A Dictionary of Quotations" edited by Suzy Platt says that this came from a letter to S Stanwood Menken in 1917 and was read by Roosevelt's sister to a national meeting that same year. Sounds legit.
Upvote:6
As was already mentioned, the quote comes from letter to S. Stanwood Menken, dated 1917-01-10. You can read the full wording of the letter at Theodore Roosevelt Digital Library. Your quote is on the page 2.