If you're a single man with infants (under age 1) and/or children (under age 5) then, THEY are eligible for the benefits of the program. Women are specifically added in because the program is designed to also help pregnant, breastfeeding and/or postpartum women who have their own nutritional needs. Women who don't meet those requirements are also not eligible.

So, you don't get help with food for yourself, but you can get assistance for infants/children ... there are other programs to help you.

Search terms used on Google in Incognito mode: single man with children WIC eligibility
Brings you to this page: https://www.joinproviders.com/state/illinois/wic/
Which has the below information:
There are four kinds of eligibility for WIC:

1. Categorical: you need to be a mom, child, or have custody of a child.

Moms have to be pregnant, up to six months past pregnancy, or up to your baby’s first birthday if you’re breastfeeding.

Children are eligible up to their fifth birthday.

Foster parents, guardians and single fathers who have custody of their children are also eligible.

1. Residential: You need to live in the state where you’re applying.

2. Nutritional: A health professional needs to determine if you are at “nutrition risk.” This might mean you have a medical condition like anemia, or a diet that could be healthier. You can see a health professional for free at a local WIC clinic.

3. Financial: Your household needs to make less than the amounts listed in the income limit table below to qualify for WIC. A pregnant woman counts as two (or more) household members. If you know you’re having more than one baby, count each one as a household member.

The top link for that search is for a page in IL, but I saw similar for other states.

If you have an infant or child I believe you can.