Can an acid have a high pH?
No, acids can't have pH greater than 7. By definition, at 25 °C, solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic.

In your question you say thiopental and pH = 10.5. Actually this is sodium thiopental with pH range of 10.2-11.2 for a 8% solution SOURCE. The solution is alkaline because of hydrolysis.

The pH value however can be less than 0 or greater than 14 for very strong acids and bases respectively. (Lim, Kieran F. (2006). "Negative pH Does Exist". Journal of Chemical Education. 83 (10): 1465.)