I do have a page in which i have a embedded YouTube video.I would like to share this video in the corresponding users twitter account.Is there any means by which I could share this YouTube video in a twitter account.?Could I perform this process using some API..?Hope someone could really help me with this.
You haven't really provided any information which is indicative of your current set-up, but generally speaking adding Tweet button is extremely easy using the Twitter API.
Twitter actually provides a great button generator which you can use to generate the relevant HTML embed code here.
You can read more about the Tweet button API here