Answer: Yes.

“HPV (also known as Genital warts) is not preventable by any contraceptive, including condoms.”
–From a Congressional Report by the U.S. Centers for Disease Control and Prevention  

You are at risk for contracting a STI, regardless of which type of contraceptive you use.

Hormonal Contraceptives (i.e. birth control pills, shot, patch, ring)

• Do not prevent STIs
• Actually alter the female genital tract, increasing a woman's risk of contracting Chlamydia (a bacterial STI) and HIV

Barrier Contraceptives (i.e.condoms, diaphragm, cervical cap)

• Can increase vaginal infection, increasing STI risk
• People who use condoms have "safe" sex more often, increasing their risk of STI exposure

Citation: US Centers For Disease Control and Prevention. 
http://www.cdc.gov/std/hiv/STDFact-STD&HIV.htm

• Using birth control actually INCREASES your risk of getting an STI by 30%.
• Abstinence is the only 100% effective way to prevent STIs and pregnancy.