Only tracks that have been purchased via iTunes can be added to your projects. The song becomes available for use as soon as it has the Play button instead of Purchased visible next to it in the Music > iTunes > iTunes Library section. It might require some technical time for the button to update depending on iTunes functioning. As soon as the purchased item is available for use, it will be listed right under the search bar in Your Library section of Splice.
If the button still states Purchased and not Play after a few hours or days, don't hesitate to contact iTunes support.