Yes, you can. Now both on your Facebook Page as well as on your personal profile.
When you’re writing a new post, instead of clicking Publish, click the drop down menu and you’ll find a Schedule option. You can schedule a post from 10 minutes to 6 months in advance.
Not in a distant past it was only possible to schedule a post on a Facebook Page. Now it has changed and every Facebook user can schedule post on their personal profile. To do that you have to start creating a new post and then some icons and options will appear on the left side of ‘Post’ button. One of them – the last one – is calendar icon. When you click it you will be able to set the date (year, month, day) when you’d like the post to be published.