Try this code
var path: String = NSBundle.mainBundle().pathForResource("nameOfFile", ofType: "svg")!
var url: NSURL = NSURL.fileURLWithPath(path) //Creating a URL which points towards our path
//Creating a page request which will load our URL (Which points to our path)
var request: NSURLRequest = NSURLRequest(URL: url)
webView.loadRequest(request) //Telling our webView to load our above request