WordPress doesn’t have “tweeting” functionality built in. However, post scheduling is built in. You just set the time when you want the post to publish on the edit post screen.
If you use a twitter plugin like my own Simple Twitter Connect, and you schedule a post, then it will send the tweet at the same time as the post is published. STC requires some setup, but the STC-Publish module, using auto-publish, will support scheduled posts just fine.
The only downside is that scheduling itself uses the WP-Cron mechanism, which is more a of “best-effort” mechanism than an actual scheduler. The WP-Cron system fires based on people visiting the site. So if nobody visits the site, then the schedule can vary.
For example, say you schedule a post for 6pm. If nobody visits the site until 7pm, then the post publish doesn’t happen until 7pm, and the tweet sent by STC also won’t occur until 7pm. No way around this, really, the WP-Cron system relies on there being traffic to the site to trigger it into action.