You're question is phrased oddly.
Unsure if you're trying to...
1) Auto post Facebook content to a WordPress site... or...
2) Auto post WordPress content to a Facebook page.
My guess is #2, so you'll use https://hootsuite.com or something similar.
You must be very careful about how exactly you do this, as you'll either destroy your WordPress site SEO or Facebook page SEO.
Before you start down this path, best hire someone like a Fractional CMO (Chief Marketing Officer) to go through your entire online ecosystem + money flow, to ensure you're optimizing your marketing aligned with your exact income goals.