Running Wordpress in a subdirectory (not the root)
Adding these lines to .htaccess should do the job (not tested, sorry, it may not be sufficient):
RewriteEngine OnRewriteCond %{HTTP_HOST} ^(www.)?mysite.com$RewriteRule ^(/)?$ wp [L]
Update: You might wish to check https://codex.wordpress.org/Giving_WordPress_Its_Own_Directory for a way to accomplish this that's closer to WordPress standards.