Generally, in Virginia a parent cannot relinguish parental rights unless there is a step-parent willing to adopt the child or if both natural parents give up rights to adoptive parents.
Keep in mind also that although you may be able to voluntarily relinquish parental rights, you may not always be able to get out of paying child support. This is a delicate issue and would require some planning.
If you have no relationship with the child, and all parties are in agreement that you should be out of the child's life, with no continued visitation or support, then you may be able to accomplish this goal with an agreed order giving the natural mother sole legal and physical custody, terminating any visitation to you, and making an agreed order to waive child support. You will always run the risk, however, that she can ask the court to modify that child support order at some point in the future, because child support is fully modifiable with a showing of a material change in circumstances since the last order.