Yevhen Horbyshyn

This plugin allows you to send Telegram messages when posts are published. You can configure which post types trigger notifications, and customize your bot credentials and chat ID.
<h3>External services</h3>
This plugin connects to an API to send message to Telegram messenger.
It sends the message every time new post of chosen type added. 
This service is provided by Telegram Messenger Inc “Telegram”: Terms of use – https://telegram.org/tos, privacy policy – https://telegram.org/privacy.

HQFam Post Notifier for Telegram

Send Telegram notifications when WordPress posts are published — simple and configurable plugin.

Ameer Mousavi

Hi, 
Whether you want to receive notifications about your website (e.g. comment submit, user register, new core update and etc.) or you just want to share your posts/products in Telegram Channel; you are welcome to use this plugin. This will help you to integrate Telegram with WordPress.
This plugin based on <a href="http://notifcaster.com" rel="nofollow ugc">Notifcaster</a> service by Ameer Mousavi and allows WordPress site to send notifications to telegram.
Note: You have to turn on WordPress email notifications in order to receive Telegram notifications. Because in this version you will receive the body of any email that WordPrss is sending.
Please feedback and rate to make this plugin better.
Here is a <a href="http://ameer.ir/telegram-for-wp" rel="nofollow ugc">Persian Tutorial</a>

Telegram for WP

Allows WordPress site to send notifications to Telegram. You can also send files/posts/products to Telegram Channel.

HQFam Post Notifier for Telegram vs Telegram for WP