要设置跨账户访问AWS API Gateway，您需要完成以下步骤：

1. 在目标账户中创建一个API，并获取该API的资源ID。

2. 在源账户中创建一个IAM角色，并为该角色创建一个信任策略，允许目标账户中的API Gateway服务扮演该角色。

下面是一个使用Python SDK（boto3）的代码示例，演示如何创建信任策略和IAM角色：

import boto3
import json

source_account_id = 'YOUR_SOURCE_ACCOUNT_ID'
target_account_id = 'YOUR_TARGET_ACCOUNT_ID'
api_gateway_resource_id = 'YOUR_API_GATEWAY_RESOURCE_ID'

def create_iam_role():
    iam_client = boto3.client('iam')
    
    trust_policy = {
        "Version": "2012-10-17",
        "Statement": [
            {
                "Effect": "Allow",
                "Principal": {
                    "AWS": f"arn:aws:iam::{target_account_id}:root"
                },
                "Action": "sts:AssumeRole"
            }
        ]
    }
    
    response = iam_client.create_role(
        RoleName='CrossAccountAPIGatewayRole',
        AssumeRolePolicyDocument=json.dumps(trust_policy)
    )
    
    return response['Role']['Arn']

def attach_policy_to_role(role_arn):
    iam_client = boto3.client('iam')
    
    response = iam_client.attach_role_policy(
        RoleName='CrossAccountAPIGatewayRole',
        PolicyArn='arn:aws:iam::aws:policy/AmazonAPIGatewayInvokeFullAccess'
    )

def create_resource_policy(role_arn):
    api_gateway_client = boto3.client('apigateway')
    
    resource_policy = {
        "Version": "2012-10-17",
        "Statement": [
            {
                "Effect": "Allow",
                "Principal": {
                    "AWS": role_arn
                },
                "Action": "execute-api:Invoke",
                "Resource": f"arn:aws:execute-api:*:*:{api_gateway_resource_id}/*"
            }
        ]
    }
    
    response = api_gateway_client.put_rest_api_policy(
        restApiId='api_gateway_id',
        policy=json.dumps(resource_policy)
    )

role_arn = create_iam_role()
attach_policy_to_role(role_arn)
create_resource_policy(role_arn)

请将代码中的YOUR_SOURCE_ACCOUNT_ID、YOUR_TARGET_ACCOUNT_ID和YOUR_API_GATEWAY_RESOURCE_ID替换为适当的值。

此代码示例将在源账户中创建一个名为CrossAccountAPIGatewayRole的IAM角色，并将允许目标账户使用该角色。然后，它将在API Gateway中创建一个资源策略，允许该角色访问指定的API资源。

确保您的代码在具有适当的权限的环境中运行，并使用正确的AWS凭证进行身份验证。