  We derive the universal relations for an ultracold two-component Fermi gas
with spin-orbit coupling (SOC)
$\sum_{\alpha,\beta=x,y,z}\lambda_{\alpha\beta}\sigma_{\alpha}p_{\beta}$, where
$p_{x,y,z}$ and $\sigma_{x,y,z}$ are the single-atom momentum and Pauli
operators for pseudo spin, respectively, and the SOC intensity
$\lambda_{\alpha\beta}$ could take arbitrary value. We consider the system with
an s-wave short-range interspecies interaction, and ignore the SOC-induced
modification for the value of the scattering length. Using the first-quantized
approach developed by S. Tan (Phys. Rev. Lett. \textbf{107}, 145302 (2011)), we
obtain the short-range and high-momentum expansions for the one-body real-space
correlation function and momentum distribution function, respectively. For our
system these functions are $2\times2$ matrix in the pseudo-spin basis. We find
that the leading-order ($1/k^{4}$) behavior of the diagonal elements of the
momentum distribution function (i.e., $n_{\uparrow\uparrow}({\bf k})$ and
$n_{\downarrow\downarrow}({\bf k})$) are not modified by the SOC. However, the
SOC can significantly modify the behavior of the \textit{non-diagonal elements}
of the momentum distribution function, i.e., $n_{\uparrow\downarrow}({\bf k})$
and $n_{\downarrow\uparrow}({\bf k})$, in the large-$k$ limit. In the absence
of the SOC, the leading order of these elements is ${\cal O}(1/k^{6})$. When
SOC appears, it can induce a term on the order of $1/k^{5}$. We further derive
the adiabatic relation and the energy functional. Our results show the SOC can
induce a new term in the energy functional, which simply describe the
contribution from the SOC to the total energy. The form of the adiabatic
relation for our system is not modified by the SOC.
