A bit mindblowing: put the browser itself in the cloud: Mighty [Hacker News discussion].
The External SAEF module lets you use a form on an ExpressionEngine template to insert a row into any database table — whether into your EE installation’s own database or into any to which you have administrator access. It may help you integrate EE with other MySQL-based systems, such as a commerce platform.
For more information, and an important warning, see the docs.
If you need to insert data into a database without an entry form, see the External Entries plugin.