What is the easiest way to run python scripts in a cloud server?
Since you said that performance is a problem and you are doing web-scraping, first thing to try is a Scrapy framework - it is a very fast and easy to use web-scraping framework. scrapyd tool would allow you to distribute the crawling - you can have multiple scrapyd services running on different servers and split the load between each. See:
There is also a Scrapy Cloud service out there:
Scrapy Cloud bridges the highly efficient Scrapy development environment with a robust, fully-featured production environment to deploy and run your crawls. It's like a Heroku for Scrapy, although other technologies will be supported in the near future. It runs on top of the Scrapinghub platform, which means your project can scale on demand, as needed.
As an alternative to the solutions already given, I would suggest Heroku. You can not only deploy easily a website, but also scripts for bots to run.
Basic account is free and is pretty flexible.
This blog entry, this one and this video contain practical examples of how to make it work.
There are multiple places where you can do that. Just google for "python in the cloud", you will come up with a few, for example https://www.pythonanywhere.com/.
In addition, there are also several cloud IDEs that essentially give you a small VM for free where you can develop your code in a web-based IDE and also run it in the VM, one example is http://www.c9.io.