Can be about 20% faster by using just one comparison per char and for instead of foreach:
bool isDigits(string s) 
{ 
    if (s == null || s == "") return false; 
    for (int i = 0; i < s.Length; i++) 
        if ((s[i] ^ '0') > 9) 
            return false; 
    return true; 
}
Code used for testing (always profile because the results depend on hardware, versions, order, etc.):
static bool isDigitsFr(string s) { if (s == null || s == "") return false; for (int i = 0; i < s.Length; i++) if (s[i] < '0' || s[i] > '9') return false; return true; }
static bool isDigitsFu(string s) { if (s == null || s == "") return false; for (int i = 0; i < s.Length; i++) if ((uint)(s[i] - '0') > 9) return false; return true; }
static bool isDigitsFx(string s) { if (s == null || s == "") return false; for (int i = 0; i < s.Length; i++) if ((s[i] ^ '0') > 9) return false; return true; }
static bool isDigitsEr(string s) { if (s == null || s == "") return false; foreach (char c in s) if (c < '0' || c > '9') return false; return true; }
static bool isDigitsEu(string s) { if (s == null || s == "") return false; foreach (char c in s) if ((uint)(c - '0') > 9) return false; return true; }
static bool isDigitsEx(string s) { if (s == null || s == "") return false; foreach (char c in s) if ((c ^ '0') > 9) return false; return true; }
static void test()
{
    var w = new Stopwatch(); bool b; var s = int.MaxValue + ""; int r = 12345678*2; var ss = new SortedSet<string>(); //s = string.Concat(Enumerable.Range(0, 127).Select(i => ((char)i ^ '0') < 10 ? 1 : 0));
    w.Restart(); for (int i = 0; i < r; i++) b = s.All(char.IsDigit); w.Stop(); ss.Add(w.Elapsed + ".All .IsDigit"); 
    w.Restart(); for (int i = 0; i < r; i++) b = s.All(c => c >= '0' && c <= '9'); w.Stop(); ss.Add(w.Elapsed + ".All <>"); 
    w.Restart(); for (int i = 0; i < r; i++) b = s.All(c => (c ^ '0') < 10); w.Stop(); ss.Add(w.Elapsed + " .All ^"); 
    w.Restart(); for (int i = 0; i < r; i++) b = isDigitsFr(s); w.Stop(); ss.Add(w.Elapsed + " for     <>");
    w.Restart(); for (int i = 0; i < r; i++) b = isDigitsFu(s); w.Stop(); ss.Add(w.Elapsed + " for     -");
    w.Restart(); for (int i = 0; i < r; i++) b = isDigitsFx(s); w.Stop(); ss.Add(w.Elapsed + " for     ^");
    w.Restart(); for (int i = 0; i < r; i++) b = isDigitsEr(s); w.Stop(); ss.Add(w.Elapsed + " foreach <>");
    w.Restart(); for (int i = 0; i < r; i++) b = isDigitsEu(s); w.Stop(); ss.Add(w.Elapsed + " foreach -");
    w.Restart(); for (int i = 0; i < r; i++) b = isDigitsEx(s); w.Stop(); ss.Add(w.Elapsed + " foreach ^");
    MessageBox.Show(string.Join("\n", ss)); return;
}
Results on Intel i5-3470 @ 3.2GHz, VS 2015 .NET 4.6.1 Release mode and optimizations enabled:
time    method          ratio
0.7776  for     ^       1.0000 
0.7984  foreach -       1.0268 
0.8066  foreach ^       1.0372 
0.8940  for     -       1.1497 
0.8976  for     <>      1.1543 
0.9456  foreach <>      1.2160 
4.4559  .All <>         5.7303 
4.7791  .All ^          6.1458 
4.8539  .All. IsDigit   6.2421 
For anyone tempted to use the shorter methods, note that