Not directly in SSRS.

If you create your own ASP.NET page with the report control you can use a text box with AJAX or similar technology to achieve this effect.

By itself, SSRS won't do it, and it's not really meant to be a search engine.

The best way to help your users is to use the "available values" of a parameter. You can provide a dataset to the available values which will populate the parameter drop-down list. It's best to keep these lists short for usability reasons.

Another option is that you take a free-text parameter and work it into a query somewhat like this

where databasecolumn like '%' + parameter + '%'

But I don't recommend that last option. It's too open ended and while it looks helpful to your users it's really not. Providing them a drop-down list is far better.