I would like to know how can I make this action in SP 2013 ?
Hoping your help,
You can download the page from site collection source, and upload the page in site collection destination.
Or you can make a granular backup of the pages library (site collection source) in Central Administration, and restore the pages library in site collection destination if you don't have any other pages you need to save in that library.
Or you can backup the entire site collection using Backup-SPSite powershell script and run Restore-SPSite to another web application (with another content database) in the same farm.
It really depends on what you're trying to accomplish by copy a page, library or site.
Here is what I would do, copy and paste the page using two sessions of SharePoint designer.
Open the first site in SharePoint designer and navigate to the wiki page in the site pages library. Then do the same for the second site. Copy and Paste the page from one site to another.
Also note that any web parts that rely on lists or data from the first site collection may not work as expected.
I found a similar answer on Stackoverflow and changed it for your requirements:
One of the options could be to save a Wiki site as a site template. Then deploy it in a site collection and to create new sites from it. But unfortunately since Wiki site is Publishing based site, it is not supported to Save Site as Template.
But there is another option - moving sites via Site Content and Structure:
Site Settings, then
Content and structure (under Site Administration)
copyaction in the context menu
Copydialog select a destination (parent site) and then click
See reference post here: https://stackoverflow.com/questions/25103249/how-to-move-wiki-pages-between-sites-in-sharepoint-2013