After the Alabasta Arc, when Robin had joined the crew, Roronoa Zoro initially distrusted her, but later on he demonstrates that he cares for her too, as he is willing to fight for her when she is in danger, such as catching her when she was nearly killed by Enel and furiously attacking him for harming her; being the first one to jump to her aid when she was threatened by Aokiji; and jumping to her aid and protected her from getting killed by Hyouzou and said he would fight him in her place.
Furthermore, just like the rest of her friends, he fought to save her from Enies Lobby and won the key that eventually set her free. Robin herself is willing to protect him in any kind of danger he is in, such as how she desperately tried to save him from getting killed by Kizaru and stopping him from being killed by the water pressure when he wanted to exit the ship on the way towards Fishman Island. After Enies Lobby, Zoro completely trusts Robin and they both get along well with each other.
Amongst the crew, Zoro and Robin are the most calm and serious in any situation. Robin is also the only person amongst the crew that never gets on Zoro’s nerves nor angers him over anything due to their similar personalities. Coincidentally, two of Zoro’s more notable displays of power: Asura in Enies Lobby, and the 1080-pound cannon in Dressrosa, came as a direct response to Robin’s safety.