The explosive growth of artificial intelligence (AI) workloads in modern data centers demands a radical transformation of interconnect architectures. Traditional copper and optical wiring face fundamental challenges in latency, power consumption, and rigidity, constraining the scalability of distributed AI clusters. This article introduces a vision for Terahertz (THz) Wireless Data Center (THz-WDC) that combines ultra-broadband capacity, one-hop low-latency communication, and energy efficiency in the short-to-medium range (1-100m). Performance and technical requirements are first articulated, including up to 1 Tbps per link, aggregate throughput up to 10 Tbps via spatial multiplexing, sub-50 ns single-hop latency, and sub-10 pJ/bit energy efficiency over 20m. To achieve these ambitious goals, key enabling technologies are explored, including digital-twin-based orchestration, low-complexity beam manipulation technologies, all-silicon THz transceivers, and low-complexity analog baseband architectures. Moreover, as future data centers shift toward quantum and chiplet-based modular architectures, THz wireless links provide a flexible mechanism for interconnecting, testing, and reconfiguring these modules. Finally, numerical analysis is presented on the latency and power regimes of THz versus optical and copper interconnects, identifying the specific distance and throughput domains where THz links can surpass conventional wired solutions. The article concludes with a roadmap toward wireless-defined, reconfigurable, and sustainable AI data centers.