This paper proposes an analog orthogonal frequency division multiplexing (OFDM) architecture based on the real-time Fourier transform (RTFT). The core enabling component is a linear-chirp phaser with engineered group velocity dispersion (GVD), which realizes RTFT and performs frequency-to-time mapping in the analog domain. In this architecture, conventional digital fast Fourier transform (FFT) and inverse FFT (IFFT) processors are replaced by two linear-chirp phasers with opposite group delay dispersions, respectively. Theoretical analysis demonstrates that, under specific phaser conditions, the OFDM signal generated by the RTFT-based analog system is mathematically equivalent to that of a conventional digital OFDM system. This equivalence is further supported by simulation results, which confirm accurate symbol transmission and recovery, as well as robustness to multipath fading when a prefix is applied. Benefiting from the use of passive microwave components, the analog OFDM system offers ultra-fast processing with reduced power consumption. Overall, this work establishes a foundation for fully analog or hybrid analog-digital OFDM system, offering a promising solution for next-generation high-speed, wideband, and energy-efficient wireless communication platforms.