Fractional-order control (FOC) has gained significant attention in power system applications due to their ability to enhance performance and increase stability margins. In grid-connected converter (GCC) systems, the synchronous reference frame phase-locked loop (SRF-PLL) plays a critical role in grid synchronization for renewable power generation. However, there is a notable research gap regarding the application of FOC to the SRF-PLL. This paper proposes a fractional-order SRF-PLL (FO-SRF-PLL) that incorporates FOC to accurately track the phase angle of the terminal voltage, thereby improving the efficiency of grid-connected control. The dynamic performance of the proposed FO-SRF-PLL is evaluated under varying grid conditions. A comprehensive analysis of the small-signal stability of the GCC system employing the FO-SRF-PLL is also presented, including derived small-signal stability conditions. The results demonstrate that the FO-SRF-PLL significantly enhances robustness against disturbances compared with the conventional SRF-PLL. Furthermore, the GCC system with the FO-SRF-PLL maintains stability even under weak grid conditions, showing superior stability performance over the SRF-PLL. Finally, both simulation and experimental results are provided to validate the analysis and conclusions presented in this paper.