"作打油诗的人" can be translated into English as "a person who writes doggerel" or simply "a doggerel writer".
"Doggerel" refers to humorous, often nonsensical, and usually poorly written verse, which aligns with the characteristics of "打油诗" (dá yǒu shī) in Chinese.
"A person who writes doggerel" or "a doggerel writer" directly describes someone who engages in the creation of such poetry.