Sorry for being inactive for few days, here's the one I made, It'll return the index of an option based on the needed string, not the value. I just thought there's an easy function to do the process but I think there's none. just in case, this will do.
HTML
<select id = "myDropDown">
<option>I</option> //0
<option>Love</option> //1
<option>my</option> //2
<option>granny<option> //3
</select>
Javascript
var dropDownList = document.getElementById("myDropDown");
var str = "granny";
var i =0;
for(i=0;i<dropDownList.length;i++){
if(dropDownList.options[i].text == str){
console.log("index: " + i);
}
}