1 to 10:
[0-9]{1,10}
In .NET (and not only, see the comment below) also valid (with a stipulation) this:
\d{1,10}
C#:
var regex = new Regex("^[0-9]{1,10}$", RegexOptions.Compiled);
regex.IsMatch("1"); // true
regex.IsMatch("12"); // true
..
regex.IsMatch("1234567890"); // true
regex.IsMatch(""); // false
regex.IsMatch(" "); // true
regex.IsMatch("a"); // false
P.S. Here's a very useful sandbox.