  We find that the minor axes of the ultra-diffuse galaxies (UDGs) in Abell
2634 tend to be aligned with the major axis of the central dominant galaxy, at
a $\gtrsim 95\%$ confidence level. This alignment is produced by the bright
UDGs with the absolute magnitudes $M_r<-15.3$ mag, and outer-region UDGs with
$R>0.5R_{200}$. The alignment signal implies that these bright, outer-region
UDGs are very likely to acquire their angular momenta from the vortices around
the large-scale filament before they were accreted into A2634, and form their
extended stellar bodies outside of the cluster; in this scenario, the
orientations of their primordial angular momenta, which are roughly shown by
their minor axes on the images, should tend to be parallel to the elongation of
the large-scale filament. When these UDGs fell into the unrelaxed cluster A2634
along the filament, they could still preserve their primordial alignment signal
before violent relaxation and encounters. These bright, outer-region UDGs in
A2634 are very unlikely to be the descendants of the high-surface-brightness
dwarf progenitors under tidal interactions with the central dominant galaxy in
the cluster environment. Our results indicate that the primordial alignment
could be a useful probe of the origin of UDGs in large-scale structures.
