I know this is old and closed question, but the solution mentioned here didn't help me.
So i'll post the solution here for ppl like me in hope it will help them.
The thing you need to do is set the Alignment property AFTER the Text property (see the code below).
var p1 = document.Paragraphs.Add(System.Reflection.Missing.Value);
p1.Range.Font.Name = "Calibri";
p1.Range.Font.Size = 18;
p1.Range.Text = "right";
p1.Range.ParagraphFormat.Alignment = Word.WdParagraphAlignment.wdAlignParagraphRight;
p1.Range.InsertParagraphAfter();
var p2 = document.Paragraphs.Add(System.Reflection.Missing.Value);
p2.Range.Font.Name = "Calibri";
p2.Range.Font.Size = 16;
p2.Range.Text = "center";
p2.Range.ParagraphFormat.Alignment = Word.WdParagraphAlignment.wdAlignParagraphCenter;
p2.Range.InsertParagraphAfter();
var p3 = document.Paragraphs.Add(System.Reflection.Missing.Value);
p3.Range.Font.Name = "Calibri";
p3.Range.Font.Size = 14;
p3.Range.Text = "left";
p3.Range.ParagraphFormat.Alignment = Word.WdParagraphAlignment.wdAlignParagraphLeft;
p3.Range.InsertParagraphAfter();
This is the way it worked for me.