According to this list from the Justice Department's Bicentennial Celebration of the United States Attorneys, the US Attorney for the Western District of Texas for the years you are researching were:
C.T. Garland 1871-1871 and Andrew J. Evans 1872-1885. No US Attorney is listed for 1870.
I hope this is helpful in your research!
The National Archives at Fort Worth holds the Records of the U.S. District Courts for the Western District of Texas. The finding aid for the records can be found here. If you are interested in researching any of these records please contact the National Archives at Fort Worth at: firstname.lastname@example.org.
Best of luck in your research!