РЕШЕНИЕ 1 (КРОСС-БРАУЗЕР)

function GetProperty(classOrId,property){ 
    var FirstChar = classOrId.charAt(0);  var Remaining= classOrId.substring(1);
    var elem = (FirstChar =='#') ?  document.getElementById(Remaining) : document.getElementsByClassName(Remaining)[0];
    return window.getComputedStyle(elem,null).getPropertyValue(property);
}

alert(  GetProperty(".my_site_title","position") ) ;

РЕШЕНИЕ 2 (КРОСС-БРАУЗЕР)

function GetStyle(CLASSname) {
    var styleSheets = document.styleSheets;
    var styleSheetsLength = styleSheets.length;
    for(var i = 0; i < styleSheetsLength; i++){
        if (styleSheets[i].rules ) { var classes = styleSheets[i].rules; }
        else { 
            try {  if(!styleSheets[i].cssRules) {continue;} } 
            //Note that SecurityError exception is specific to Firefox.
            catch(e) { if(e.name == 'SecurityError') { console.log("SecurityError. Cant readd: "+ styleSheets[i].href);  continue; }}
            var classes = styleSheets[i].cssRules ;
        }
        for (var x = 0; x < classes.length; x++) {
            if (classes[x].selectorText == CLASSname) {
                var ret = (classes[x].cssText) ? classes[x].cssText : classes[x].style.cssText ;
                if(ret.indexOf(classes[x].selectorText) == -1){ret = classes[x].selectorText + "{" + ret + "}";}
                return ret;
            }
        }
    }
}

alert(GetStyle('.my_site_title'));