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Abstract Relativistic magnetic turbulence has been proposed as a process for producing nonthermal particles in high-energy astrophysics. The particle energization may be contributed by both magnetic reconnection and turbulent fluctuations, but their interplay is poorly understood. It has been suggested that during magnetic reconnection the parallel electric field dominates the particle acceleration up to the lower bound of the power-law particle spectrum, but recent studies show that electric fields perpendicular to the magnetic field can play an important, if not dominant role. In this study, we carry out two-dimensional fully kinetic particle-in-cell simulations of magnetically dominated decaying turbulence in a relativistic pair plasma. For a fixed magnetization parameterσ₀ = 20, we find that the injection energyε_injconverges with increasing domain size toε_inj ≃ 10m_ec². In contrast, the power-law index, the cut-off energy, and the power-law extent increase steadily with domain size. We trace a large number of particles and evaluate the contributions of the work done by the parallel (W_∥) and perpendicular (W_⊥) electric fields during both the injection phase and the postinjection phase. We find that during the injection phase, theW_⊥contribution increases with domain size, suggesting that it may eventually dominate injection for a sufficiently large domain. In contrast, on average, both components contribute equally during the postinjection phase, insensitive to the domain size. For high energy (ε ≫ ε_inj) particles,W_⊥dominates the subsequent energization. These findings may improve our understanding of nonthermal particles and their emissions in astrophysical plasmas.