How to show wordpress recent posts on vBulletin pages?

what you could do is if vbb allows you to call an rss feed, to pull the feed and display the recent entries that way.

How to show wordpress rss in vbulletin?

I think your question would be better answered by vBulletin folk:

https://www.vbulletin.com/forum/

Are there any variable we can append to wordpress rss feeds so it only shows the posts url without summary?

No, not really. For that you’d need to edit out the <description> and <content> tags from the feed file. But if this is for incorporating into vBulletin, it may have a way of specifying what elements of a feed are displayed.