Precise needle alignment is essential for percutaneous needle insertion in robotic ultrasound-guided procedures. However, inherent challenges such as speckle noise, needle-like artifacts, and low image resolution make robust needle detection difficult, particularly when visibility is reduced or lost. In this paper, we propose a method to restore needle alignment when the ultrasound imaging plane and the needle insertion plane are misaligned. Unlike many existing approaches that rely heavily on needle visibility in ultrasound images, our method uses a more robust feature by periodically vibrating the needle using a mechanical system. Specifically, we propose a vibration-based energy metric that remains effective even when the needle is fully out of plane. Using this metric, we develop a control strategy to reposition the ultrasound probe in response to misalignments between the imaging plane and the needle insertion plane in both translation and rotation. Experiments conducted on ex-vivo porcine tissue samples using a dual-arm robotic ultrasound-guided needle insertion system demonstrate the effectiveness of the proposed approach. The experimental results show the translational error of 0.41$\pm$0.27 mm and the rotational error of 0.51$\pm$0.19 degrees.