It is correct, but a little unusual
In "I have it learned", the word "learned" is a participle phrase (consisting of just one word". Compare this sentence with "I have it in my hand" (referring to a pencil) or "I have it cooked perfectly" (referring to a pie).
The structure of "I have it learned" and "I have it in my hand" are analogous and they communicate in the same way. The italicized part is a predicate asserted about "it". With the participle learned, there is also a suggestion that the speaker did the learning, though this could be overridden by context.
So since "learn" means "store in memory", this means "I have [the script] (stored in my memory)". It is correct, but usually you would want to say "I have learned it" (meaning almost the same but using the present perfect).