Translation:There is an option to do a search on the site.
That sounds more like the search of a crime scene than of a website, though. Actually, I suppose the most colloquial thing to say about a website would be "it is searchable."
If you really must use the phrase "a possibility" it has to go with the gerund, not the infinitive: "There's a possibility of searching the site." Still very awkward, but at least correct.