As GanesanSenthilvel said use a List<string> instead or the Array.Resize() method.
Here are some examples:
List<string> dataFile = new List<string>();
dataFile.AddRange(File.ReadAllLines(FileName));
then you could add another files lines in the same way
dataFile.AddRange(File.ReadAllLines(SomeOtherFile));
or
string[] data = new string[] { "blah", "blah blah", "blah blah blah" };
dataFile.AddRange(data);
or a single line
dataFile.Add("some line of data");
or
string someData = "blah blah blah blah";
dataFile.Add(someData);
You could if you really wanted to use the Array.Resize() method i.e.
string[] data = new string[2];
data[0] = "some data";
data[1] = "some more data";
Array.Resize(ref data, data.Length + 1);
data[2] = "even more data";