Is content promotion needed in modern SEO? If I use my content to promote it on the social media sites then it can be crawled as copied content on my website. What is the right way of content promotion?

Content promotion through SMO has needed in 2014 seo as these sites are playing great role in SERP ranking. If you use whole content then definitely it will be treated as duplicate content. The best way is to edit title and little bit content as well while submitting in SMO sites.

content promotion is not so effective rather than using unique and informative content in different seo activities or social media activities,use of such content in appropriate manner would also led to establish the business as well as to get the traffic

I don't agree with Smiti. Content Promotion is essential for the modern SEO. It helps you to increase traffic and visitor to your site. If you share or promote your content through your social media channel it wll not be treated as duplicate.
One common example is Search Engine Land.

commented: I agree with Deepanshu +0

Content Marketing is done effectively nowadays and it gives a good result.When you haven't posted any of the content for submission then you can share it in social media sites.You should post your website link only once in your social media sites and not many times.

Yes, it is important to gain more traffic and visitors.

yes content promotion is also important. It will increase the ranking of the keywords and it also increase the traffic to your website.

In my point of veiw content promotion is also an important part.