To create the list from scratch, use LINQ:
ids.Split(',').Select(i => int.Parse(i)).ToList();
If you already have the list object, omit the ToList() call and use AddRange:
myList.AddRange(ids.Split(',').Select(i => int.Parse(i)));
If some entries in the string may not be integers, you can use TryParse:
int temp;
var myList = ids.Split(',')
.Select(s => new { P = int.TryParse(s, out temp), I = temp })
.Where(x => x.P)
.Select(x => x.I)
.ToList();
One final (slower) method that avoids temps/TryParse but skips invalid entries is to use Regex:
var myList = Regex.Matches(ids, "[0-9]+").Cast<Match>().SelectMany(m => m.Groups.Cast<Group>()).Select(g => int.Parse(g.Value));
However, this can throw if one of your entries overflows int (999999999999).