post image in Instagram

No, you can't. Quoted from Instagram API docs :

At this time, uploading via the API is not possible. We made a conscious choice not to add this for the following reasons:

1. Instagram is about your life on the go – we hope to encourage photos from within the app. However, in the future we may give whitelist access to individual apps on a case by case basis.
2. We want to fight spam & low quality photos. Once we allow uploading from other sources, it's harder to control what comes into the Instagram ecosystem. All this being said, we're working on ways to ensure users have a consistent and high-quality experience on our platform.

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UPDATE: However, if you're working on iOS (though you tagged Android), there is a way to "send" a photo (in fact, it opens the image in Instagram) via Custom URL Scheme. See this.

Yet it is not possible to post image in Instagram like FB or twitter.

But this is another way to achieve this using already installed Instagram and if not this will notify user to download app .

 public void onClick(View v) {

        Intent intent = getPackageManager().getLaunchIntentForPackage("com.instagram.android");
        if (intent != null)
        {
            Intent shareIntent = new Intent();
            shareIntent.setAction(Intent.ACTION_SEND);
            shareIntent.setPackage("com.instagram.android");
            try {
                shareIntent.putExtra(Intent.EXTRA_STREAM, Uri.parse(MediaStore.Images.Media.insertImage(getContentResolver(), imagePath, "I am Happy", "Share happy !")));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            shareIntent.setType("image/jpeg");

            startActivity(shareIntent);
        }
        else
        {
            // bring user to the market to download the app.
            // or let them choose an app?
            intent = new Intent(Intent.ACTION_VIEW);
            intent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
            intent.setData(Uri.parse("market://details?id="+"com.instagram.android"));
            startActivity(intent);
        }

    }