  Starting from a type II superstring model defined on $R^{2,2}\times CY_6$ in
a linear graviphoton background, we derive a coordinate dependent $C$-deformed
${\cal N}=1$, $d=2+2$ superspace. The chiral fermionic coordinates $\theta$
satisfy a Clifford algebra, while the other coordinate algebra remains
unchanged. We find a linear relation between the graviphoton field strength and
the deformation parameter. The null coordinate dependence of the graviphoton
background allows to extend the results to all orders in $\alpha'$.
