Indeed the API does not have a method setBackgroundRGB(string), provides a method setBackgroundRGB(Integer, Integer, Integer), however, an option to achieve what you need, having a string as input is:
function setColorToRange() {
var colorRGB = '0, 255, 0';
var ss = SpreadsheetApp.getActiveSpreadsheet();
var sheet = ss.getActiveSheet();
var range = sheet.getRange('A1:B3');
range.setBackgroundRGB.apply(range, colorRGB.split(', '));
}
UPDATE
To get the vector can be applied several improvements, widening a little the example presented, we integrate some of the improvements indicated in the comments, resulting in the following:
function setColorToRange() {
var colorRGB = '0, 255, 0';
var ss = SpreadsheetApp.getActiveSpreadsheet();
var sheet = ss.getActiveSheet();
var range = sheet.getRange('A1:B3');
var arrColorRGB = getRGB(RGBString);
range.setBackgroundRGB.apply(range, arrColorRGB);
}
function getRGB(RGBString) {
// Returns a vector of integers
return RGBString.replace(/ /g, '').split(',').map(returnInt);
}
function returnInt(value) {
return parseInt(value, 10);
}