  For a mixture of alkali-earth atomic gas in the long-lived excited state
${}^3P_0$ and ground state ${}^1S_0$, in addition to nuclear spin, another
"orbital" index is introduced to distinguish these two internal states. In this
letter we propose a mechanism to induce Feshbach resonance between two atoms
with different orbital and nuclear spin quantum numbers. Two essential
ingredients are inter-orbital spin-exchanging scattering and orbital dependence
of the Land\'e g-factors. Here the orbital degrees of freedom plays similar
role as electron spin degree of freedom in magnetic Feshbach resonance in
alkali-metal atoms. This resonance is particularly accessible for ${}^{173}$Yb
system. The BCS-BEC crossover in this system requires two fermion pairing order
parameters, and displays significant difference comparing to that in
alkali-metal system.
