After the Alabasta Arc, when Robin had joined the crew, Zoro was the only one not to trust her (he was the only one she could not bribe, hold debt to, or 'charm'). However, later on, he shows a willingness to protect her if she is in any danger, such as catching her when she was nearly killed by Enel and being the first one to jump to her aid when she was threatened by Aokiji.
After the Enies Lobby Arc, Zoro completely trusts Robin and they both get along well with each other. Like for the rest of the crew, Zoro would risk his life to protect her too. 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