You can split the value of the multi-line textbox and then add each part as one row.
[UPDATE] Added code from comment
DataTable dt = new DataTable();
dt.Columns.Add("ABCD", typeof(string));
string parts[] = textBox1.Split(new char[] { '\r', '\n' }, StringSplitOptions.RemoveEmptyEntries);
foreach (string part in parts)
{
dt.Rows.Add(part);
}