Use a parameter array with the params modifier:

public static int AddUp(params int[] values)
{
    int sum = 0;
    foreach (int value in values)
    {
        sum += value;
    }
    return sum;
}

If you want to make sure there's at least one value (rather than a possibly empty array) then specify that separately:

public static int AddUp(int firstValue, params int[] values)

(Set sum to firstValue to start with in the implementation.)

Note that you should also check the array reference for nullity in the normal way. Within the method, the parameter is a perfectly ordinary array. The parameter array modifier only makes a difference when you call the method. Basically the compiler turns:

int x = AddUp(4, 5, 6);

into something like:

int[] tmp = new int[] { 4, 5, 6 };
int x = AddUp(tmp);

You can call it with a perfectly normal array though - so the latter syntax is valid in source code as well.