Connections between information theory and thermodynamics have proven to be very useful to establish bounding limits for physical processes. Ideas such as Landauer's erasure principle and information-assisted work extraction have greatly contributed not only to broadening our understanding about the fundamental limits imposed by nature, but also paving the way for practical implementations of information-processing devices. The intricate information-thermodynamics relation also entails a fundamental limit on parameter estimation, establishing a thermodynamic cost for information acquisition. We show that the amount of information that can be encoded in a physical system by means of a unitary process is limited by the dissipated work during the implementation of the process. This includes a thermodynamic tradeoff for information acquisition. Likewise, the information acquisition process is ultimately limited by the second law of thermodynamics. This tradeoff for information acquisition may find applications in several areas of knowledge.