With a so-called "thin" credit file, you won't get much traction on your quest for personal credit. Even if you have accounts with Canadian companies that maintain a presence in the United States, those firms' American divisions act independently of their home offices.
However, Capital One now markets a Cash Rewards for Newcomers MasterCard. The card carries a high APR, but no annual fee. Therefore, you'll get the most value by using it to cover everyday purchases and travel expenses that you plan to pay off at the end of each statement cycle. As the youngest of the country's biggest credit card issuers, Capital One prides itself on maintaining its own consumer database and underwriting new accounts based on information beyond what's in your credit report.
Unlike a typical instant approval credit card offer, Capital One will take some extra time to verify your employment and residency status. According to company officials, if you've got a job with a reputable company and you've been renting a home, you're very likely to get accepted. With no foreign transaction fee, you'll be able to use this card when you visit friends and family back north. After a few years with this MasterCard, you'll qualify other Capital One credit cards. By that time, you'll probably get plenty of low introductory rate credit card offers in the mail.
Additionally, Bank of America and Wells Fargo both offer secured credit cards for less than $40 a year. Like the Newcomers card, they'll carry interest rates much higher than you might be used to. By placing a few hundred dollars on deposit, you'll get a positive trade line on your credit report that you can use to get an unsecured credit card in about a year.