  Recent experiments show that $\Delta\gamma$, an observable designed for
detecting the chiral magnetic effect (CME), in small collision system $p+A$ is
similar with that in heavy ion collision $A+A$. This brings a challenge to the
existence of CME because it is believed that there is no azimuthal correlation
between the orientation of the magnetic field ($\Phi_B$) and the participant
plane ($\Phi_2$) in small collision system. In this work, we introduce three
charge density models to describe the inner charge distributions of proton and
neutron, and calculate the electric and magnetic fields produced in small $p+A$
collisions at both RHIC and LHC energies. Our results show that the
contribution of the single projectile proton to the magnetic field is the main
source after average over all participants. The azimuthal correlation between
$\Phi_B$ and $\Phi_2$ is small but not vanished. And due to the huge
fluctuation of fields strength, the magnetic-field contribution to
$\Delta\gamma$ could be large.
