How do I teleport a player to another entity while changing the player's rotation?

When teleporting a entity to another, you cannot change the rotation. (There is no way to achieve this in a single command)

/tp @p @e[type=ArmorStand]

However, if you make this command run right after/before the teleportation to the armor stand, you can achieve the same effect.

/tp @p ~ ~ ~ <x rotation> <y rotation>

(Teleports the person who uses this command nowhere, then changes his rotation, or vice versa.)
Clue: Try making the armor stand execute this command.^

^ Since you're using @p, it does not affect the armor stand.

(for 1.13+)

What I have found is:

/execute at @e[type=pig] as @e[pig,limit=1,sort=nearest] run tp @s @p

Seems to teleport the entity while keeping the player's rotation. (teleports entity with the player's original rotation)