how manyth is not a phrase that would be used. but i don't think there's a single word that could be used in that context. to use rank would imply that one president was more important than another.
you'd have to ask in what order he was as a president.
i.e. was he the 5th or 6th president?
or how many presidents were there before him?
if that helps any

I came across a way to say this:

Süleyman Demirel Türkiyenin kaçıncı cumhurbaşkanıydı?

What number president of Turkey was Süleyman Demirel?

Does this sound OK to native English speakers?

What about asking like this:

In the chronologic order what number was Süleyman Demirel as the president of Turkey?

btw I agree with many of comments, english linguists should consider adding "how manyth"  to the language since this question form exists in nearly all of the languages but not in english.

 Sorry, no. It smells like translation, as do most of all of the other suggestions.

The problem is not in how to translate it. It is the fact that, in England at least, we do not have the concept of numbering our monarchs or prime ministers. So, for example, at the moment you don´t hear BBC news saying anything like "Gordon Brown was the 75 th prime minister of Britain" or "David Cameron is carrying on talks with Nick Clegg in an attempt to become the 76th prime minister"

For the same reason, although the suggestion "in chronological order, which number ...." makes linguistic sense in English, it doesn´t mak much common sense.

I think we are trying to solve an impossible problem, like how do you make water run uphill?

We just don´t have the concept in England.

Now, I know the Americans number their presidential administrations. Can an American help us with how you would ask the question in a constitutional history exam???

Marion,

Actually I came across this usage in the following question? Does it sound OK to you in the following case?

A group of friends are standing in a circle, playing a game.
They proceed around the circle, chanting a rhyme and pointing
at the next person (clockwise) on each word. When the rhyme finishes
whoever is being pointed at leaves the circle. They then start again,
pointing where they left off, and the game continues
until only one person is left. He/She is declared the winner.

For example, suppose there are six friends (numbered 1 to 6) standing around
the circle and the rhyme is "Eenee, Meenee, Mainee, Mo!". They begin with player number 1.
The first person to leave the circle is number 4, followed by 2 then 1, 3 and 6.
Number 5 is left (draw it out to see it first hand).

Using this pattern, what number player, beginning with player 1,
is the last person standing in a game played with 100,000 players?

 Yes, it makes sense. You have used seven words in English (not just the one in Turkish) "what number player beginning with player 1" to explain the concept. This is what I meant, you have to explain it "round the houses" rather than just one word, because their isn´t the one word concept in English.

A real stickler for English grammar might point out that as they are different numbers, that can be individually identified, it should be "which" not "what"

which number player, beginning with player 1

OK but where is just one in Turkish? Seven words in English can be translated as follows

Which number player, beginning with player 1 = 1´den başlayarak kaçıncı oyuncu

that sounds fine to me. People will understand what you mean. It only sounds a little awkward because "of Turkey" is in the middle. I would just say "What number president was Süleyman Demirel"

OK. I included Turkey because I was trying to translate it word by word.