What high limit student cards can I get without a deposit?

There are no high limit unsecured student credit cards. Typically, student credit cards have much lower credit limits than other credit cards, most carrying minimum credit limits of $300 or so.

One of the best student credit cards is the Bank of America Travel Rewards Credit Card for Students, with its 25,000-point initial bonus for spending $1,000 within 90 days of account opening, redeemable for $250 in travel expenses. It also provides 3 points for every $1 in purchases made through the Bank of America's Travel Center as well as 1.5 points per $1 spent on all other purchases. This card charges neither an annual fee nor a foreign transaction fee.

With this said, while your card might have a credit limit of, say, $1,500, it's wise to keep your balance under 30% of your limit to maintain a good credit utilization ratio and protect your score.