Psychic powers and magic, as separate systems, can be found together in the Marvel and DC universes. I suspect one could find the same thing in pulps such as Doc Savage.
If we define psychic powers as uncanny abilities that depend upon the internal power of the individual and not on external sources such as gods, spirits, incantations, rituals, or objects then they can be found in the European tradition:
Galadriel's ability to read minds in The Lord of the Rings. Tolkien's inspiration here was Ayesha in H Rider Haggard's She.
Mesmerism or animal magnetism
The evil eye
Second sight
It could also be argued that by the definition above the powers of gods and other non-human entities such as fairies are psychic.