This assumes you have already configured the aws command line tool. If not, check out my article on Getting Started with the AWS CLI.

The aws ec2 associate-route-table command can be used to update the Route Table being used by one of your Subnets in one of your Virtual Private Clouds (VPCs).

~]$ aws ec2 associate-route-table --route-table-id rtb-0e96e9343c4086863 --subnet-id subnet-0f015da3a1e164304
{
    "AssociationState": {
        "State": "associated"
    },
    "AssociationId": "rtbassoc-03280f7a1a677851b"
}