We propose a N=2 twisted superspace formalism with a central charge in four
dimensions by introducing a Dirac-Kähler twist. Using this formalism, we
construct a twisted hypermultiplet action and find an explicit form of
fermionic scalar, vector and tensor transformations. We construct a off-shell
Donaldson-Witten theory coupled to the twisted hypermultiplet. We show that
this action possesses N=4 twisted supersymmetry at on-shell level. It turns out
that four-dimensional Dirac-Kähler twist is equivalent to the Marcus's twist.