  Most stars form in clusters where relatively close encounters with other
stars are common and can leave imprints on the orbital architecture of
planetary systems. In this paper, we investigate the inclination excitation of
debris disk particles due to such stellar encounters. We derive an analytical
expression that describes inclination excitation in the hierarchical limit
where the stellar flyby is distant. We then obtain numerical results for the
corresponding particle inclination distribution in the non-hierarchical regime
using a large ensemble of N-body simulations. For encounters with expected
parameters, we find that the bulk inclination of the disk particles remains
low. However, a distinct high inclination population is produced by prograde
stellar encounters for particles with final pericenter distances above $50$AU.
The maximum extent $i_t$ of the inclination distribution scales with the
inclination of the encounter $\sin(i_s)$ for massive star flybys with low
incoming velocity. The inclination distribution of observed trans-Neptunian
objects places constraints on the dynamical history of our Solar System. For
example, these results imply an upper limit on product of the number density
$n$ of the solar birth cluster and the Sun's residence time $\tau$ of the form
$n\tau\lesssim8\times10^4$ Myr pc$^{-3}$. Stronger constraints can be derived
with future observational surveys of the outer Solar System.
