  The spin-dependent twist-3 and 4 nucleon matrix elements d^(2) and f^(2)
describing power corrections to the Bjorken and Ellis-Jaffe sum rules are
computed in the instanton vacuum. A systematic expansion in the small packing
fraction of the instanton medium, rho / R << 1, is performed. We find that the
twist-3 matrix element d^(2) is suppressed [of order (rho / R)^4], while the
twist-4 matrix element f^(2) is of order unity. Numerically, d^(2) << f^(2).
The small value of d^(2) \sim 10^{-3} obtained from instantons is consistent
with the recent E143 measurements of the structure function g_2, where d^(2)
enters at the same level as the twist-2 contribution.
