The way you can do this is get an allen key for whatever bridge type you have.... If it's a strat style bridge or a Floyd Rose style bridge that has individual saddles... all you have to do is detune the strings... and adjust each saddle by raising it. Start with very very very small amounts. If you raise it too much you may knock the intonation off slightyl... So raise all the bridge saddles by giving it a quarter to a half of a turn. Retune the strings play the notes that are around the high frets and see if it helped... You can repeat the process as necessary... or until the action is getting too high for your comfort level.
Just another suggestion. If you don't feel comfortable you can take it to a tech and they will do the adjustment and probably give you a full set-up which inculdes adjusting the intonation of the guitar...
Good Luck