  ALMA observations have detected extended ($\simeq 10$ kpc) [C II] halos
around high-redshift ($z \gtrsim 5$) star-forming galaxies. If such extended
structures are common, they may have an impact on the line intensity mapping
(LIM) signal. We compute the LIM power spectrum including both the central
galaxy and the [C II] halo, and study the detectability of such signal in an
ALMA LIM survey. We model the central galaxy and the [C II] halo brightness
with a S\'ersic+exponential profile. The model has two free parameters: the
effective radius ratio $f_{R_e}$, and the central surface brightness ratio,
$f_{\Sigma}$, between the two components. [C II] halos can significantly boost
the LIM power spectrum signal. For example, for relatively compact [C II] halos
($f_\Sigma=0.4$, $f_{R_{\rm e}}=2.0$), the signal is boosted by $\simeq 20$
times; for more extended and diffuse halos ($f_\Sigma=0.1, f_{R_{\rm e}}=6.0$),
the signal is boosted by $\simeq 100$ times. For the ALMA ASPECS survey
(resolution $\theta_{\rm beam} = 1.13''$, survey area $\Omega_{\rm
survey}=2.9\,\rm arcmin^{2}$), the [C II] power spectrum is detectable only if
the deL14d [C II] - SFR relation holds. However, with an optimized survey
($\theta_{\rm beam} = 0.232''$, $\Omega_{\rm survey}=2.0\,\rm deg^{2}$), the
power spectrum is detectable for almost all the [C II] - SFR relations
considered in this paper. Such a survey can constrain $f_\Sigma$ ($f_{R_{\rm
e}}$) with a relative uncertainty of $\sim 15\%$ ($\sim 10\%$). A successful
LIM experiment will provide unique constraints on the nature, origin, and
frequency of extended [C II] halos, and the [C II] - SFR relation at early
times.
