No, you don't need to fear this; God won't reject you because your parents weren't married when you were born. After all, you weren't responsible for what they did, and God doesn't hold us accountable for situations we can't control. We're only responsible for our own sins, not the sins of others.
Elsewhere in your letter, you mention the fears you've had over the years, wondering if your biological parents rejected you because they didn't think you were worth keeping. But this news should convince you otherwise! Undoubtedly your parents knew they couldn't provide for you, and they did what they felt was best for you. Giving you up for adoption was an act of love on their part, not an act of rejection.
The most important truth I can tell you, however, is that God loves you and accepts you just as you are. He loves you so much that His Son came into the world to give His life for you. If you've never done so, respond to His love by turning to Christ in repentance and faith, and asking Him to come into your life.
When we come to Christ, He not only forgives us but He adopts us into His family. The Bible says, "How great is the love the Father has lavished on us, that we should be called children of God! And that is what we are!" (1 John 3:1). Open your heart to Christ today.