D&D 5E - Player angry about enemies climbing rope with Rope Trick

Mechanically, the orcs and orogs could do as you state. There is absolutely nothing wrong with the orcs and orogs going up the rope as a natural part of the encounter - so long as it makes sense given the knowledge of the orcs and orogs. If, for example, the ranger cast the spell out of sight of the orcs and orogs and climbed it without being seen, and the orcs and orogs have no knowledge of the spell, then having them climb the rope would be pushing contrivance.

Regardless, your word choice invokes a tone that would be concerning for me to hear as a player in your game.

...The Ranger cried foul and claims I cheated, but I think that was RAW. The player tried a metagaming power move and was taken to the woodshed.

Am I wrong?

Taking a player to the woodshed is clearly a reference to punitive action. Kids taken to the woodshed, once upon a time, were spanked for misbehavior. You're essentially indicating that you did this to punish the player.

Further, you're doing it as a response to a 'metagaming power move'. This confuses me as there is nothing in the tale you told that seems to reference metagaming by the player (what outside knowledge did the player use?) Regardless of whether metagaming was the right description for the transgression you see, you are punishing the player for what you deem to be bad action.

As a DM you should never punish a player or their character because you are displeased. You have all the power. The game world is shaped by your whim. Players trust their DMs to use that power fairly - and using it to punish them, when they have not power and you have all the power is an overxtension of the power dynamic. In fact, you should be very careful to avoid even the appearance of misuing power. DMs should always show their players respect and reinforce the player's trust in the DM.

That is not to say that the DM has no place in shaping the actions of the players at the table. If you consider a player's actions to be inappropriate, you should take some action. If it is offensive, then that action may need to be immediate (such as when a player makes another player uncomfortable), but if not offensive (as in the case where a PC pushes a rule boundary or fails to follow play dynamics that the rest of the group shares), it can usually wait until between sessions where you can talk about it in private.

This is also not to say that an NPC / bad guy can't punish a PC as part of the story you're telling. Good villians would create emotional responses from the PCs. However, it should not be a response to your perceptions, as a DM, of the game, but instead be part of the natural story of the game and something that grows organically out of the story being told - and even then it needs to be done within the comfort levels of the players at the table.