Will applying for a second zero percent credit card now affect the rate on the first one?

I have a $26,000 balance on a home equity loan which has a rate of 8.75%. My goal was to transfer the entire balance to a zero percent credit card for the promotional one year and pay it off interest free before the year is up. I have been accepted for only $9000 from Discover. Will applying for and accepting another credit card affect the interest rate on this card? It does mention something in the T&C about them checking my credit periodically and if anything changes affecting my credit (a.i. delinquent accounts, late pays, etc.). This might affect my credit ratios (amount of available credit).