docs(cli): Add Claude Code integration section

docs/CLI_INTEGRATION.md

@@ -8,3 +8,39 @@ This guide explains how to connect popular AI command-line tools to **CLIProxyAP
 - You must have the appropriate client keys (e.g., Anthropic API key, OpenAI API key) configured in the proxy or provided via headers.
 
 ---
+
+## Claude Code (Anthropic CLI)
+
+Claude Code can be easily routed through the proxy by setting the `ANTHROPIC_BASE_URL` environment variable.
+
+### Configuration via Environment Variables
+
+Set the following variables in your terminal or shell profile (`.bashrc`, `.zshrc`):
+
+```bash
+# Point Claude Code to the proxy
+export ANTHROPIC_BASE_URL="http://localhost:7860/v1"
+
+# Your API key (can be your real key or a proxy-specific key)
+export ANTHROPIC_API_KEY="your-api-key-here"
+```
+
+### Configuration via Settings File
+
+Alternatively, you can modify `~/.claude/settings.json`:
+
+```json
+{
+  "anthropicBaseUrl": "http://localhost:7860/v1"
+}
+```
+
+### Running Claude Code
+
+Once configured, simply run:
+
+```bash
+claude
+```
+
+---