The relative sunspot number (SN) is the primary index of solar activity back to 1610. For earlier periods, SN can be reconstructed from the concentrations of cosmogenic isotopes, particularly 14C and 10Be in natural archives. However, due to the limitations of measurement techniques, these reconstructions typically provide SN with only decadal resolution. We aim to reconstruct the first annually resolved sunspot numbers for the first millennium BC, providing a detailed view of solar cycles over a period when this was not possible before. Methods. We reconstruct sunspot numbers from high-precision annual measurements of relative decay-corrected ^14^C concentrations, {Delta}^14^C, covering 1000-BC (Brehm et al. 2025). The process is based on the physics-based approach developed by Usoskin et al. (2021A&A...649A.141U, Cat. J/A+A/649/A141) and has the following four steps: (1) inverting the carbon-cycle model to reconstruct the production rate of ^14^C, Q; (2) accounting for the effect of the varying geomagnetic field on Q; (3) computing the open solar magnetic flux; and (4) converting it into sunspot numbers. A Monte-Carlo approach is used to account for the uncertainty of the reconstruction. We reconstructed annually resolved SN covering the first millennium BC. Over that period, we identified 93 complete solar cycles with a mean length of 10.5 years. Among those cycles, 23 are well- defined, 21 are reasonably defined, while the rest are poorly defined. We found strong agreement between our reconstructed SN and previous decadal reconstructions, though with higher SN around 1000-920 BC. We did not find any significant long-term periodicities beyond the 11-year solar cycle. Conclusions. This reconstruction offers unique insights into cyclic solar activity for this period of time, which will be valuable for solar dynamo studies and irradiance modelling