My ex sister-in-law has given up my 9 year old nephew to my care, and wants nothing more to do with him.
Can I adopt him if not what else can I do,

You might be able to adopt, but it requires a lot of work and her permission, and the biological father has to be found or a long, serious attempt to find him has to be made. You really need an adoption lawyer. It's not something that can be changed if someone changes their mind.

How was he given up to your care? A child is not a piece of property that can be given away.

Yes you may be able to adopt him, but your first concern is having the legal right to care for him.

To add to what Scott said, your second concern is to get him into counseling. At his age he is going to have some abandonment issues.

Do you have legal guardianship yet?

He was living with his dad, until 1st may this year when he drop dead,(my brother} that's when he went to live with his mother.
Two night ago we had a text, telling me that if I didn't pick him up he was going in care, and yes I agree they are not something you toss to side when you get fed up of them.

So you have NO legal right to care for the child. So, Monday morning you should be in court filing for temporary guardianship. Get that wrapped up and then see where you go.