Is there a way to store items?

Player stash is being added in version 1.07.

Adds a stash for player convenience. Players can now store loot in their stash, access to which is available in different parts of the world. Stash locations are marked on the map.

Source: http://thewitcher.com/news/view/1081

EDIT

For the sake of updating my answer, the ability to store items was added in patch v1.07.

Adds a stash for player convenience. Players can now store loot in their stash, access to which is available in different parts of the world. Stash locations are marked on the map.

You can easily find these stash that have a green chest symbol easily spotted on the map. Something like this:

The Saddlebags are also important though :D

OLD VERSION

No you cannot.

So far there is no way of storing your items like you did in The Witcher 2: Assassins of Kings. Maybe CD Projekt RED will include it in an Enhanced Version or in a future Patch.

Basically to increase your limit of weight carrying you should buy SaddleBags

If you want to know about saddlebags there is already a question about this here.