Add OpenRouter integration (#40004)

Co-authored-by: c0ffeeca7 <38767475+c0ffeeca7@users.noreply.github.com>

source/_integrations/open_router.markdown

@@ -0,0 +1,37 @@
+---
+title: OpenRouter
+description: Instructions on how to integrate OpenRouter as a conversation agent
+ha_category:
+  - Voice
+ha_release: 2025.8
+ha_iot_class: Cloud Polling
+ha_config_flow: true
+ha_codeowners:
+  - '@joostlek'
+ha_domain: open_router
+ha_integration_type: service
+ha_platforms:
+  - conversation
+---
+
+The [OpenRouter](https://openrouter.ai/) {% term integration %} allows you to use the OpenRouter API as a conversation agent in Home Assistant.
+
+This integration provides a way to interact with a wide range of AI models available on OpenRouter, while billing is handled by OpenRouter.
+You can even use your own third-party (like OpenAI) API key.
+
+{% include integrations/config_flow.md %}
+
+## Generate an API Key
+
+The API key is used to authenticate requests to OpenRouter. To generate an API key take the following steps:
+
+- Log in to [OpenRouter](https://openrouter.ai/) or sign up for an account.
+- Go to the **API Keys** section in your account settings.
+- To generate a new key, select **Create API Key**.
+- Give the key a name, and be sure to set up billing limits.
+
+## Removing the integration
+
+This integration follows standard integration removal, no extra steps are required.
+
+{% include integrations/remove_device_service.md %}