Hi,
there is no actual split tool I know of for this task, but you can run the tool Filter SAM or BAM, output SAM or BAM twice, once keeping only the reads on the forward strand, once keeping those on the reverse strand.
For the forward strand reads:
Filter on bitwise flag: yes
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Skip alignments with any of these flag bits set (the second of the two multiselect panels)
For the reverse strand reads:
Filter on bitwise flag: yes
-
Only output alignments with all of these flag bits set (the first of the two multiselect panels)
Rationale behind this (since your question made me realize that the checkbox name Read strand (and Mate strand just below it) used in the tool interface are really not that helpful): the 5th bit in the SAM/BAM FLAG field is set to 1 if the read sequence stored in the BAM file is the reverse-complement of the originally determined sequence indicating that the read mapped to the rerverse strand (see the SAM/BAM format specification).