  In this paper, we study the anomalous flavor changing neutral current Yukawa
interactions between the top quark, the Higgs boson, and either an up or charm
quark ($\rm tqH, q=u, c$). We probe these couplings in $\rm e^- p\rightarrow
\nu_e \bar{t} \rightarrow \nu_e H \bar{q}$ and the channel $\rm e^- p
\rightarrow \nu_e H b$. Both channels are induced by charged current
interactions through $\rm e^- p$ collision at the Large Hadron Electron
Collider(LHeC). We study the signatures with the Higgs decay modes $\rm
H\rightarrow \gamma\gamma, b\bar{b}$ and $\tau^+\tau^-$. Our results show that
the flavor changing couplings $\rm \kappa_{tqH}$ can be probed down to a value
of 0.0162 in $\rm e^- p \rightarrow \nu_e \bar{t} \rightarrow \nu_e H \bar{q}$
with $\rm H\rightarrow b \bar{b}$ at a 14 TeV LHeC with a 150 GeV electron beam
and 200 $\rm fb^{-1}$ luminosity. This value of the coupling corresponds to the
branching ratio $\rm Br(t\rightarrow qH)=1.34 \times 0^{-4}$.
