Yes zinc does. In a study (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3649098/) men ranging from 27 to 60 years old were evaluated to determine if zinc plays a role in serum testosterone levels. First they restricted men with healthy zinc levels from dietary zinc and measured their testosterone levels also they supplement men with deficient zinc levels and then measured their testosterone levels. Considering the biological relevance of zinc with testosterone production the results are not surprising. The men who were deficient of a proper diet with zinc levels saw their testosterone levels drop by almost 75% after 20 weeks. Additionally, men who already deficient with zinc saw their testosterone levels increase by 100% after 24 weeks of zinc supplementation.
Another study confirmed the prior observation here https://www.ncbi.nlm.nih.gov/pubmed/21671089. In this a direct of comparison of zinc levels was measured against testosterone levels in a group of random. The age of men in this group ranged from 40 to 60 years old. Researchers observed that the men having a normal testosterone level typically had an elevated level of zinc compared with others who had a low level of testosterone.
The studies used synthetic sources of zinc such as zinc gluconate. There are tons of all natural sources of zinc. Generally speaking beans, lentils, nuts and oatmeal are good choices.
