As Stuart mentioned, HTTPS can sometimes have a small positive impact on page rankings (it’s thought that it is likely used as a tie breaker when two pages rank very closely), however, I’d like to add that HTTPS should not be used as an SEO strategy in and of itself especially if you ever consider transitioning an entire website over to it. Transferring an entire website to HTTPS can cause more harm than good if it isn’t done extremely carefully.
It’s best to look at HTTPS as an improvement to user security.
Can HTTPS hurt your SEO?
In your case, HTTPS will not have any negative effect on your SEO. If you’re interested in understanding the concept a little deeper, here is how it can.
How HTTPS can harm your SEO:
If we have a page called “example.com” and some of the inbound links pointing to it are written as http://example.com and others are written as https://example.com, it’s likely that Google will end up indexing both the secure and insecure versions of the pages, creating duplicate content.
The main issue here is that when your inbound links are split between two identical pages, the Page Authority becomes diluted (say 40% of links point to HTTPs and 60% point to HTTP). Ideally, all inbound links should point to a single page that you are trying to rank, giving it the largest boost possible.
Hope that helps!