How can I use bigint with C#?

You can use System.Numerics.BigInteger (add a reference to System.Numerics assembly). As mentioned in the comments this might not be the right approach though.

Native support for big integers has been introduced in .NET 4.0. Just add an assembly reference to System.Numerics, add a using System.Numerics; declaration at the top of your code file, and you’re good to go. The type you’re after is BigInteger.

Here's using BigInteger. This method Prints Numbers in the Fibonacci Sequence up to n.

public static void FibonacciSequence(int n)
{
    /** BigInteger easily holds the first 1000 numbers in the Fibonacci Sequence. **/
    List<BigInteger> fibonacci = new List<BigInteger>();
    fibonacci.Add(0);
    fibonacci.Add(1);
    BigInteger i = 2;
    while(i < n)
    {                
        int first = (int)i - 2;
        int second = (int) i - 1;

        BigInteger firstNumber =  fibonacci[first];
        BigInteger secondNumber = fibonacci[second];
        BigInteger sum = firstNumber + secondNumber;
        fibonacci.Add(sum);
        i++;
    }         

    foreach (BigInteger f in fibonacci) { Console.WriteLine(f); }
}

BigInteger is available in .NET 4.0 or later. There are some third-party implementations as well (In case you are using an earlier version of the framework).

Better use System.Numerics.BigInteger.