It really depends on how you want your community to look and feel, but as some general advice, I would encourage you to be cautious. Icons next to usernames are very prominent and consideration should be made to only using them for very special members of the community, such as your moderators, community manager and superusers. If they are overused they will obviously lose their impact.
@Karlee92 great question and I totally agree with @JasonHill's wise advice. That being said, there are some communities who have opted to display a rank icon for each rank, the top icons obviously being the most prestigious. Here's an example from HP Inc's Support Forum: http://h30434.www3.hp.com/t5/Miscellaneous-Topics-Read-Only/HP-Support-Forum-Ranking-Overview/m-p/6#...
Some brand names and rank naming conventions align more naturally to iconography than others. For example, I worked with a community team who chose a fun fish theme for their ranks (ex. minnow -> king mackerel -> whale shark). Each rank name had a icon of that fish. Their community is private, otherwise I'd link you to it
Since you'll need to create the icons, consider the LOE for your team. Naturally, the more ranks you add, the higher LOE.