Every person is different. There is no way to predict how long it will take. We don't know what all your child has experienced. Moving into a new home is a huge adjustment for a child. Even if the child is happy and thankful to be adopted there still may be some hesitation in your interactions. Time will be your friend in this. It has a way of healing old wounds and puts distance between people and bad experiences they have had. The more time passes, the more you will fall into a routine that your child can learn to rely on. Once your child knows that he can depend on you, you should see him start to come around.
One very real possibility is that the child is scared to get close to you. He could be scared that you're not going to stick around for long. It's likely that he feels like any connection with you will be a betrayal to his birth parents. No matter what the history is there is a strong connection that doesn't disappear when they are separated.
It could be that your child loves you and just doesn't know how to show it. Some children are never taught how to show others love. As sad as it is to think about, some kids have never known love at all. The best thing you can do is gently guide him in a way that doesn't seem uncomfortable or intrusive.
Whatever you do, do not push. You can encourage and find things the two of you can do together. You can get excited about all the things that interest your child. You can't force it though. If you get intense about it, you will be met with resistance. You go 60 percent and let him come the other 40. Focus on getting to know each other having fun and the bond will come.