Motivated by recent experimental development, we investigate spin-orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the density-matrix renormalization group method, we calculate momentum distribution function, gap, and spin-correlation function to reveal rich ground-state properties. We find that spin-orbit coupling (SOC) can generate unconventional momentum distribution, which depends crucially on the filling. We call the corresponding phase with zero gap the SOC-induced metallic phase. We also show that SOC can drive the system from the antiferromagnetic to ferromagnetic Mott insulators with spin rotating. As a result, a second-order quantum phase transition between the spin-rotating ferromagnetic Mott insulator and the SOC-induced metallic phase is predicted at the strong SOC. Here the spin rotating means that the spin orientations of the nearest-neighbor sites are not parallel or antiparallel, i.e., they have an intersection angle $theta in (0,pi )$. Finally, we show that the momentum $k_{mathrm{peak}}$, at which peak of the spin-structure factor appears, can also be affected dramatically by SOC. The analytical expression of this momentum with respect to the SOC strength is also derived. It suggests that the predicted spin-rotating ferromagnetic ($k_{mathrm{peak}% }<pi /2$) and antiferromagnetic ($pi /2<k_{mathrm{peak}}<pi $) correlations can be detected experimentally by measuring the SOC-dependent spin-structure factor via the time-of-flight imaging.
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