  Dust grains drift through the interstellar medium (ISM) and are aligned with
the magnetic field. Here we study the effect of grain alignment and grain
motion on grain growth in molecular clouds (MCs). We first discuss the
characteristic timescales of alignment of the grain axis of maximum inertia
($\hat{a}_{1}$) with its angular momentum (${\bf J}$) (i.e., {\it internal
alignment}) and alignment of ${\bf J}$ with the magnetic field (${\bf B}$,
i.e., {\it external alignment}). We determine the maximum grain size with
efficient internal ($a_{\rm max,aJ}$) and external alignment ($a_{\rm max,JB}$)
for composite grains. For the MC density of $n_{\rm H}\sim 10^{3}-10^{8}\rm
cm^{-3}$, we find that external alignment can occur for very large grains, but
internal alignment only occurs for grains smaller than $a_{\rm max,aJ}\sim 2\mu
m$. The presence of iron clusters within dust grains or suprathermal rotation
increase $a_{\max,aJ}$ to $\sim 10-50\mu m$. We then study the growth of
aligned grains drifting through the gas. Due to the motion of aligned grains
across the magnetic field, gas accretion would increase the grain elongation
rather than decrease as expected from the growth of randomly oriented grains.
Coagulation by grain collisions also increases grain elongation, leading to the
increase of elongation with the grain size. The coagulation of aligned grains
forms dust aggregates that contain elongated binaries comprising a pair of
grains with parallel short axes. Grains within dust aggregates in
67P/Churyumov-Gerasimenko obtained by {\it Rosetta} have the grain elongation
increasing with the grain radius, implying that such dust aggregates might form
from aligned grains.
