We consider the design of an incentive mechanism for a principal, who is assumed to be not trustworthy, to collect informative data from privacy-sensitive individuals. The principal offers payments to incentivize participation and informative data reporting. The individuals are strategic and take into account both the payment and the cost for privacy loss during data reporting. Due to privacy concerns, an individual may be willing to report only a noisy version of the private data, resulting in quality degradation. To achieve desirable accuracy of data analysis, it is imperative for the principal to have an incentive mechanism under which the quality of the collected data is controllable. In this paper, we exploit a game-theoretic approach to the design of a payment mechanism, such that the quality of the collected data is controllable through a parameter ϵ by making sure that each individual's strategy in a Nash equilibrium is to participate and symmetrically randomize her data, while guaranteeing ϵ-differential privacy. With this design, the principal can achieve any given accuracy objective by using the payment mechanism associated with an appropriate ϵ. In contrast to most of the existing work, which considers trusted principal and thus focuses on designing truthful mechanisms, this work is the first one to consider untrustworthy principal in private data collection and quality control mechanisms in such a scenario. We also show that the total expected payment of the designed mechanism at equilibrium is asymptotically optimal in the high data quality regime.