MeshFunctions -> {"ArcLength"}partly work but missing one point.
poly = RandomPolygon[10];
arclength = ArcLength[RegionBoundary@poly]
Show[Graphics[poly],
ListPlot[Append[#, First@#] &@poly[[1]], Joined -> True,
MeshFunctions -> {"ArcLength"}, Mesh -> 10,
MeshStyle -> {Red, AbsolutePointSize[10]},
Method -> {"BoundaryOffset" -> False}]]
