There is not a migration script available for AzuraCast migration so customers and services must be moved over to MediaCP manually. 
To help with the transition you are able to keep the same streaming links after migrating using Nginx rewrite rules, we have a full guide for this here: https://www.mediacp.net/doc/admin-server-manual/administration/custom-nginx-php-configurations/#rewrite-rules-4

In the case of AzuraCast you can specifically use the following rewrite rule

1. 1. Create a new file at /usr/local/mediacp/nginx/conf.d/locations.custom
   2. Input the rewrite rules below:

        location ~ ^/radio//?([^/]+)/?([^/]+)? {
            set $stream_url https://127.0.0.1:2020/system/proxy.php?slug=$1&unique_id=$1&portbase=$1&mounturl=$2;
      
            proxy_buffering off;
            proxy_ignore_client_abort off;
            proxy_intercept_errors off;
            proxy_redirect off;
            proxy_next_upstream error timeout invalid_header;
            proxy_pass_request_headers on;
            proxy_set_header Cache-Control no-cache;
            proxy_set_header                User-Agent "$http_user_agent [ip:$remote_addr]";
            proxy_set_header                X-Forwarded-For $remote_addr;
            proxy_connect_timeout 5;
            proxy_read_timeout 15;
            proxy_max_temp_file_size 0;
            proxy_pass $stream_url;
            expires off;
            client_max_body_size 1M;
            tcp_nodelay on;
        }

             3. After saving the rewrite rules you will need to reload the nginx service by running this command:

/usr/local/mediacp/nginx/sbin/nginx -s reload

This will allow you to use links like /radio/8000/stream or /radio/servicename/stream and keep compatbility with your AzuraCast links.