Yes you definitely can.
I have been teaching in Vietnam for more than 11 years with some stints in Thailand and have met some brilliant (and some not so brilliant) Pinoy teachers around the region.
Just make sure you have some teaching experience, a TESOl/ TESL/ or CELTA teaching certificate (if you plan to teach English). If however, you'd like to teach at International Schools abroad, you would need the experience plus probably the LET certificate from the Phils.
For ESL/EFL, some schools would only accommodate native English speakers (Taiwan for instance has a policy on this) while others are more flexible -- they really don't mind as long as you've got the qualifications plus a near native speaking ability.
Also investigate the job opportunity carefully because there are employers who might take advantage of inexperienced applicants short of exploiting them -- this was told to me by other Pinoy friends who have taught in China and Thailand.
All the best.