Concept:
A silicon diode in forward bias has a voltage drop of approximately
\[
0.7\ \text{V}.
\]
Hence the resistor gets the remaining voltage.
Step 1: Calculate the voltage across the resistor.
\[
V_R=10.7-0.7
\]
\[
V_R=10\ \text{V}.
\]
Step 2: Apply Ohm's law.
\[
I=\frac{V_R}{R}
\]
\[
=\frac{10}{10\times10^3}
\]
\[
=10^{-3}\ \text{A}
\]
\[
=1\ \text{mA}.
\]
\[\begin{aligned}
\boxed{I=1\ \text{mA}}
\end{aligned}\]
Hence, option \(\mathbf{(A)}\) is correct.