Solar activity, dominated by the 11-year cyclic evolution, has been observed directly since 1610 CE. Before that, indirect cosmogenic proxy data are used to reconstruct it over millennia. Recently, the precision of radio-carbon {DELTA}^14^C measurements has improved sufficiently to allow reconstructing cyclic solar activity over millennia. We present the first detailed reconstruction of solar activity, represented here by annual sunspot numbers, during the first millennium, 1-969, CE. The reconstruction of sunspot numbers from {DELTA}^14^C was performed using a physics-based method which involves several steps: using the modern carbon-cycle box model, the ^14^C production rate, corrected for the contemporary geomagnetic shielding, was computed from the measured concentrations; The open solar magnetic flux was computed using a model of the heliospheric cosmic-ray modulation; Sunspot numbers were calculated by inverting a model of the evolution of the Sun's magnetic field. The Markov Chain Monte Carlo approach was used to directly account for different sources of uncertainty. Annual sunspot numbers were reconstructed for the first millennium CE. This period includes one extreme solar event occurring in 774 CE and one Grand solar minimum of 650-730 CE. We could identify 91 solar cycles, of which 26 were well-defined, while 24, and 41 were reasonably and poorly defined, respectively. The mean cycle length was 10.6 years, but the lengths of individual cycles vary between 8 and 15 years. The existence of empirical Waldmeier's relations remains inconclusive with this dataset. No significant periodicities were found beyond the 11-year cycle. This work fills the gap in the solar cycle statistics between the previously reconstructed first millennium BCE and the second millennium CE, providing vital constraints for the solar dynamo and irradiance models. A consistent 3-millennium-long reconstruction of sunspot numbers, based on a composite multi-proxy cosmogenic record, is pending.