Enterprise level cloud data storage is gaining importance in the area of consumer level file hostage services. Cloud storage providers are responsible for availability, accessibility and protection of the user data. A number of encrypting schemes have been proposed for encrypting the user data in cloud storage to protect unauthorized access. Most of the Attribute Based Encryption (ABE) schemes that were proposed assume that the data in cloud storage are secure and are never disclosed. However, in reality, some of the authorities may force the cloud storage providers to disclose the cloud user's secrets or personal data. In this paper, a new deniable ABE encryption scheme for cloud storage is proposed to ensure user privacy with minimized unauthorized access. A new ranking algorithm assigns a rank to each user at the time of registration based on their personal information. The rank of the user enhances the privacy and provides access control to the data stored on cloud. Each file uploaded to cloud is assigned with a rank and the file downloads only if the rank of the user matches the rank associated with the file. If rank of the user does not match then a fake file will be downloaded. Since authorities who demand for user secret cannot decide if the information they get about the user are legitimate, the cloud storage providers make sure that the individual user privacy is still protected. The ranking algorithm is also used to provide improved cloud access response time to prioritized users.