A very good reference for various forms of AC is the book Howard, Rubin: Consequences of the Axiom of Choice. This book contains a large database of various consequence of choice and tables showing relations between them.
There is also a website where you can search for relations between various forms mentioned in this book.
In this book we can find:
FORM 142. $\neg$PB: There is a set of reals without the property of Baire. Jech [1973b] p 7 and note 28.
FORM 222. There is a non-principal measure on $\mathcal P(\omega)$. Pincus/Solovay [1977] and note 147.
Then in the table which shows implications between various forms we find:
222 142 (1) Pincus [1972c]
142 222 (3) Pincus [1972c]
(1) = "The implication is provable."
(3) = "The implication is not provable in ZF".
The reference given there is:
[1972c] D. Pincus: The strength of the Hahn-Banach theorem, Proc. of the Victoria Symp. on Nonstandard Analysis, Lecture Notes in Math. 369, Springer, Heidelberg, 1973, 203-248. DOI: 10.1007/BFb0066014.
D. Pincus writes there that this implication "is due to Solovay. It is stated without proof in [20]. Since it may interest readers of this paper we include our own proof at the end of §I." Where [20] is R. M. Solovay, A model of set theory in which every set of reals is Lesbague measurable, Ann. of Math. 92 (1970), pp. 1-58.