If I understand what you want, you make an object rotate to face a vector with a rotator.
So in this case you want your player's Z (Unreal's up) to face the vector between the two points on the rope it's touching.
So if we get the two nearest points on the rope (p1 and p2 for ex):
If we do (p2-p1) and normalize it, we get the direction we want the player to turn.
Then we can use a Rotator to orient the player to that vector. In this case we want to make a Rotator from a known Z axis (The vector we just found).
And then we apply the rotator we get from that on the player.
If you want to set the forward direction too, there's a "Make Rot from ZX" that will try to orient the player to meet those two vectors.
There's a Rotator class with these functions in C++ if you're using that.
(BTW some engines like Unity just let you set the up vector of your player explicitally like "player.transform.up = ropePitch" or something)
(I could also probably explain the math going on in the background but for practical use this is all you need!)