There are some other ways that you can encourage traffic to your content that shouldn't appear as begging and will help improve the quality of the site:
Post an answer on a related question, referencing your original post. The answer should add new information and be able to stand on its own, only linking the other post for additional information.
Post a new question, referencing your original post. The question should be new and unique and be helpful to others, only referencing the original post by relation or for additional information.
Both of these options will get you additional votes on the new posts as well as (hopefully) bringing new viewers and votes to the older ones, if you make sure that these new posts are helpful and of good quality.
As Farhan mentioned, other users may happen to do these things for you on their own in the future, so having more good quality posts will help.
As a last resort, there is also a third option, which adds less quality but also doesn't provide for added reputation:
- Leave a comment on a related question/answer, which will add helpful information. Since you can't include as much in a comment, this is harder to create a useful context and so should be used with care to avoid giving the impression of begging for votes. Comments also don't get as much visibility and are more at risk of deletion.
Of course in all of these cases, it will be better if you link to posts by other users as well and not always your own. I like to think that if you link to posts by other users, others are more likely to do the same for your own.