Add Smithery CLI installation instructions and badge

Author: calclavia

README.md

@@ -3,6 +3,7 @@
 [![Python 3.12](https://img.shields.io/badge/python-3.12-blue.svg)](https://www.python.org/downloads/release/python-3120/)
 [![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
 [![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/psf/black)
+[![smithery badge](https://smithery.ai/badge/docker-mcp)](https://smithery.ai/protocol/docker-mcp)
 
 A powerful Model Context Protocol (MCP) server for Docker operations, enabling seamless container and compose stack management through Claude AI.
 
@@ -45,6 +46,14 @@ To try this in Claude Desktop app, add this to your claude config files:
 }
 ```
 
+### Installing via Smithery
+
+To install Docker MCP for Claude Desktop automatically via [Smithery](https://smithery.ai/protocol/docker-mcp):
+
+```bash
+npx @smithery/cli install docker-mcp --client claude
+```
+
 ### Prerequisites
 
 - UV (package manager)