Einstein was bothered by "action at a distance" long before the 1935 EPR paper, and it was not specific to entanglement. In his debates with Bohr at the 1927 Solvay congress he used the single slit experiment to illustrate it, see Howard, Revisiting the Einstein-Bohr Dialogue. An objective wave function describing a particle hitting the screen after passing through the slit "presupposes a very particular mechanism of action at a distance which would prevent the wave continuously distributed in space from acting at two places of the screen" [English translation of Proceedings of Solvay, quoted from Howard]. Einstein pointed out that the problem does not arise if the wave function is interpreted statistically, as describing an ensemble of particles.
However, according to Boughn's There Is No Action at a Distance in Quantum Mechanics, Spooky or Otherwise, the word "spukhafte" was only added much later, in March 3, 1947 letter to Born, where it is not specific to entanglement either. One can argue over the translation of spukhafte as "spooky", but it is the "literal" translation, and is used in the English translation of Einstein-Born correspondence available on the Internet Archive. The relevant passage is on p. 158 (emphasis mine):
"I cannot make a case for my attitude in physics which you
would consider at all reasonable. I admit, of course, that there
is a considerable amount of validity in the statistical approach
which you were the first to recognise clearly as necessary given
the framework of the existing formalism. I cannot seriously
believe in it because the theory cannot be reconciled with the
idea that physics should represent a reality in time and space,
free from spooky actions at a distance.
I am, however, not yet firmly convinced that it can really be achieved with a continuous field theory, although I have discovered a possible way of doing this which so far seems quite reasonable. The calculation difficulties are so great that I will be biting the dust long before I
myself can be fully convinced of it. But I am quite convinced
that someone will eventually come up with a theory whose
objects, connected by laws, are not probabilities but considered
facts, as used to be taken for granted until quite recently. I
cannot, however, base this conviction on logical reasons, but can
only produce my little finger as witness, that is, I offer no
authority which would be able to command any kind of respect
outside of my own hand."