Your translation is wrong, but you are right, the tense is »Perfekt«.
This german sentence is quite unique, because the mandatory accusative object is missing. It is from the movie »Das Leben der Anderen«, spoken at 1:59:12. Normally you have to tell what is arranged, but from the context in this scene it is clear, that the files (»die Akten«) are arranged. Normally it would be seen as a grammatical error to omit this accusative object, but in this situation it is so obvious, that you can make an exception.
But this missing object doesn't affect your question. But anyway, its better to analyze the complete (i.e. grammatically correct) sentence.
So here it is:
Ich habe die Akten chronologisch ordnen lassen.
Now learn, that
Ich habe ... lassen
(in Präsens: »Ich lasse ...«) is
I let ...
So the correct translation is:
I let the files arrange chronologically.
(In English present tense and past tense are equal.)
This means: It was not me who arranged the files, but I gave the order to someone else to arrange them, and my order was executed. (I let someone else do it for me.)
If you use »gelassen« instead of »lassen«, you also have to replace »ordnen« by »geordnet«. But this changes the meaning of the sentence:
Ich habe die Akten chronologisch geordnet gelassen.
I left the files in chronological order.
This means: The files already was in chronological when I found them, and I didn't change this order. i.e. I did nothing. Neither did I arrange them nor did I give the order to arrange them. I just left them how they was.