What is somebody who can "predict" or "see" into the future called?

If it is true, you are a foreseer:

FORESEE''R, n. One who foresees or foreknows.

If you believe the gift is somehow divine in nature, then you are an Oracle.

Reference: Noah Webster's American Dictionary of the English Language, 1828.

Although the word "prophet" may have a religious meaning in some contexts, it can also be used to refer to a person with non-spiritual abilities to predict the future.

prophet

A person who makes or claims to be able to make predictions:
the anti-technology prophets of doom (Oxford Dictionaries)

A person who has:

Foreknowledge of an event, especially as a form of extrasensory perception. (ODO)

is precognitive (adjective):

The woman who stepped into my office was tall, leggy, beautiful - and bewildered, "How did you know I was about to knock" "Like it says on the door, I'm a precognitive detective.

Jack Hammett, Precognitive Detective

or has precognitive abilities/ability of precognition:

"He's been dead for ten years", she said.

"Er", said Windle, but the question was already there in his larynx, "I trust Mr. Cake is in good health?"

"It's okay. Oi speaks to him occasional," said Mrs. Cake.

"I'm sorry to hear that," said Windle.

"All right, if it makes you feel any better."

"Um, Mrs. Cake? I'm finding it a little confusing. Could you...switch off...your precognition...?"

from: The Reaper Man, by Terry Pratchet

(context: Mrs. Cake has the ability of precognition, so she answers Windle's questions before he has the chance to ask them.)

Another word you could use is augur.

From Dictionary.com:

noun
1. one of a group of ancient Roman officials charged with observing and interpreting omens for guidance in public affairs.
2. soothsayer; prophet.

verb (used with object)
3. to divine or predict, as from omens; prognosticate.

A synonym of augur is auspex.

Also, predictor is someone who predicts.

How about visionary?

OD:

visionary: A person with original ideas about what the future will or could be like

There is the word prognosticator which according to Merriam Webster means one who predicts future events or developments and defined by Lexico (powered by Oxford) as a person who foretells or prophesies a future event. Although it sounds quite rare, I quite like it and the questioner has not specified if they want a rare word or a common word. Google Ngram gives a spike between 1580 and 1600 and then there's a decline in its use. But it has been in use since 1730s until now.