Yes, if you have chlamydia in one part of your body (your rectum, for instance) it can be spread to another part (your vagina.) And of course it can be passed to a partner's body as well, particularly if you're not using condoms. In fact, as Heather mentions here, you can transmit chlamydia from one part your own body to another without a partner with just, for instance, a vibrator or anything else that can carry fluids from one part of your body to another.
...the rule of thumb with sex toys and safer sex is this: if a toy cannot be boiled (silicone toys can, and so can a lot of vibrator attachments -- vibes that are one-piece and/or have batteries set into the toy usually cannot), then you need to cover it with a condom when you use it, and use a new condom with each use.
In the same post she also lays out the guidelines for deciding when it's safe (from an STI perspective) to have unprotected sex with a partner.
You just really have to be sure to use them every time, for all direct genital contact, and not even think about going without until you and your partner have been together for at least six months monogamously, practicing safer sex for that time, and each have at least TWO full and clear STI screenings under your belt. Another important way to protect against Chlamydia is to limit partners and choose exclusive relationships where you both stay current with your STI tests: if your partner you got it from had only been having sex with you over the last six months, and had had his STI tests before even talking about going without condoms, again -- it'd be pretty weird for you to contract Chlamydia.
But notice this all assumes that somehow or other you and your partner has a chlamydia infection in the first place. If you didn't have it in your rectum then switching to your vagina without washing might give you other kinds of infections it wouldn't give you that one.
That doesn't necessarily mean you or your partner haven't been keeping your commitment to monogamy -- chlamydia is considered a "silent infection" in the sense that roughly half of all infected men and three quarters of all infected women don't show any symptoms. (This doesn't mean it's not a serious infection -- in women it can cause permanent sterility even when other symptoms aren't noticed!)
Here's a link to Scarleteen's STI File on Chlamydia.
Just remember that bacterial infections are what you're likely to get with anal-to-vaginal sex, and monogamy or a partner not having STIs doesn't decrease that risk. So, with anal-to-vaginal sex, your partner really just needs to be using condoms, and switching to a new one between activities.