  We develop a general gauge invariant construction of the one-loop effective
action for supersymmetric gauge field theories formulated in ${\cal N}=1/2$
superspace. Using manifestly covariant techniques (the background superfield
method and proper-time representations) adopted to the ${\cal N}=1/2$
superspace we show how to define unambiguously the effective action of a matter
multiplet (in fundamental and adjoint representations) and the vector multiplet
coupled to a background ${\cal N}=1/2$ gauge superfield. As an application of
this construction we exactly calculate the low-energy one-loop effective action
of matter multiplet and SU(2) SYM theory on the Abelian background.
