AWS CDK is leveraging AWS CloudFormation to deploy Stacks in AWS.

In addition, AWS CDK may require some data which is being stored in a S3 Bucket named cdktoolkit-stagingbucket-*.

This is the IAM policy IAM assigning to a AWS IAM group which should be able to deploy resources via AWS CDK. Of course, depending on the resources you want to deploy, you need further IAM permissions.

{
    "Version": "2012-10-17",
    "Statement": [
        {
            "Action": [
                "cloudformation:*"
            ],
            "Resource": "*",
            "Effect": "Allow"
        },
        {
            "Action": "s3:*",
            "Resource": "arn:aws:s3:::cdktoolkit-stagingbucket-*",
            "Effect": "Allow"
        }
    ]
}

The policy gives full access to CloudFormation and all S3 Buckets named cdktoolkit-stagingbucket-*.

Another option is to additionally grant full access for all resources and their actions if the action has been triggered by CloudFormation (or CDK):

{
    "Version": "2012-10-17",
    "Statement": [
        {
            "Action": [
                "cloudformation:*"
            ],
            "Resource": "*",
            "Effect": "Allow"
        },
        {
            "Condition": {
                "ForAnyValue:StringEquals": {
                    "aws:CalledVia": [
                        "cloudformation.amazonaws.com"
                    ]
                }
            },
            "Action": "*",
            "Resource": "*",
            "Effect": "Allow"
        },
        {
            "Action": "s3:*",
            "Resource": "arn:aws:s3:::cdktoolkit-stagingbucket-*",
            "Effect": "Allow"
        }
    ]
}

Handle with care...