Since you are replacing the same chars then you should use a temp char:
string s = "aaaabcc";
s = s.Replace("a","x");
s = s.Replace("c","a");
s = s.Replace("x","c");
Edit:
Use the following code:
string s = "aaaabcc";
StringBuilder sb = new StringBuilder();
foreach(var c in s)
{
if(c == 'a')
sb.Append('c');
else if(c == 'c')
sb.Append('a');
else
sb.Append(c);
}
string outs = sb.ToString();