We have had similar questions before but this is something that is clearly of interest, so another one is fine. Firstly it depends what you mean by 'divnination' and whether you see divination as being based primarily on instinctive and intuitive faculties or whether you see it as a link to the spiritual plane, which in some way is 'paranormal'. I'm assuming the latter for much of my reply.
The usual answer that you will receive is that it's connected to Pisces - this view has been held for most of the last 100 years and stems from Alan Leo's association of Pisces with the (then) newly discovered Neptune, which he identified with the coming of the New Age (along with Uranus). 'Pisces' here is shorthand for someone with Sun in Pisces.
A slightly more sophisticated view of this would be to shift attention to Neptune and to suggest it's someone with Neptune in the 12th house (which, for many modern Astrologers, corresponds with Pisces, the 12th sign). This approach is better in my view, simply because it's planets that are the active part of Astrology, not signs (which merely modify the planet's 'energy').
Personally, I'd be more inclined to look at the Moon, which traditionally rules the 'animal' mind - our instinctive reactions. However, instinct and intuition are not necessarily a link to the spiritual plane (though they may be a necessary, if not sufficient requirement).
Othes would look to the Nodes, as these are now associated with Karma (a concept that was introduced into Western Astrology from its Indian cousin, Jyotish - again by New Age Astrologers).
An alternative, would be to look at the third/ninth house axis and planets in those houses. Traditionally these are the houses associated with divination (such as Astrology or Tarot) and with both organised and more private religious beliefs. The ninth being the 'House of God' and the third being the 'House of the Goddess' - concepts which stem from the pre-christian Hellenistic roots of horoscopic Astrology).
Whichever you take as the more likely, you need to be aware that 'one swallow doesn't make a Spring' - you need several supporting pieces of evidence from the chart which indicate such abilities. This will involve you in looking at the aspects to and from Neptune (if you use it) or the Moon or planets in appropriate Houses. If we're talking about individuals and their abilities then you've also got to consider the Ascendant.
There really isn't any agreed or obvious universal chart 'signature', which is not really surprising given the range of divination methods and psychic or paranormal abilities.
That doesn't mean it's a question without answer at the personal level - and it will be interesting to see what others think indicates their own abilities.
Edited to Add
One thing I didn't mention is that there may be a connection to 'nocturnal births' that is births between sunset and sunrise. Traditionally these hours are ruled by the Moon. Of the seven Aeclectic members who participated in the Hellenistic thread, five of them were nocturnal births. I'm a nocturnal birth and my wife who has strong psychic abilities is also a nocturnal birth (she also has a ninth house Moon in Pisces and the Moon rules her Ascendant).
I'd be interested if others who contribute to the thread and are into divination could say whether they are a night birth or a day birth just to see if I've got a representative sample here or whether it's just a fluke.
