Yes, turmeric may improve muscle recovery. The main active compound in turmeric, curcumin, has antioxidant and anti-inflammatory properties and several studies have demonstrated that 400mg - 2000mg curcumin/day can reduce muscle soreness and inflammation after exercise .
However, the research on curcumin for muscle recovery is still in its infancy. If you want to experiment with curcumin, pair it with black pepper to enhance absorption .
 Campbell, M. S., Carlini, N. A., & Fleenor, B. S. (2021). Influence of curcumin on performance and post-exercise recovery. Critical reviews in food science and nutrition, 61(7), 1152–1162. https://doi.org/10.1080/10408398.2020.1754754
 Yoon, W. Y., Lee, K., & Kim, J. (2020). Curcumin supplementation and delayed onset muscle soreness (DOMS): effects, mechanisms, and practical considerations. Physical activity and nutrition, 24(3), 39–43. https://doi.org/10.20463/pan.2020.0020